The Gemarah says that there is no definitive pesak halacha in the disagreement between Hillel and the Rabbanan is the mitzvot are to be fulfilled with כורך or independently and therefore we do both. What would Hillel wrap together? Rashi and Rashbam (115a) hold that Hillel would wrap together the Pesach, marrot and matzah. The opinion of the Rambam (8:7) however, is that Hillel would eat only the matzah and marror together.
The Tur (475) writes הרוצה לקיים מצוה מן המובחר לא יסיח עד שיעשה כריכה כהלל כדי שתעלה לו ברכת מצה ומרור לכריכה כהלל דהא משום דלא איתמר הלכתא לא כמר ולא כמר עבדינן לחומרא כתרוייהו ה"נ לענין ברכה צריכין למיעבד שיעלה לשניהם ובשיחת חולין צריך ליזהר אבל טול ברוך לא הוי הפסק. Since we are not sure if the law follows the Chachamim or Hillel, one should not talk between the beracha and korech. The Bach says the Tur means it is a nice thing to not talk and have the beracha go on korech but in reality there is no issue for one does korech as a mere zecher liMikdash but it is not the real mitzvah even according to Hillel for we do not have korban pesach and even Hillel will have to agree the mitzvot are fulfilled independently. However, the Taz (475:7) says that it would seem this is לעיכובא and if one speaks, one would have to say a new beracha. What is the peshat in the Taz?
The Gemarah proves from the fact that Hillel holds one can bundle the various mitzvot of the night with their different tastes, that he holds the tastes of various mitzvot don't nullify each other. However, that applies to mitzvot of the same level of obligation. Nowadays that there is no korban Pesach, maror is only a Rabbinic obligation and can no be consumed together with the matzah. So Hillel should be the same as the Rabbanan? Tosfos (Pesachim 115a) says according to Hillel, we would first eat matzah by itself and then eat matzah together with maror. How does Tosfos solve the issue, if you ate the matzah already you fulfilled your obligation and the maror is then going against matzah that is not obligatory? The Pri Migadim (475 M.Z. 7) says the opinion of Tosfos is like the Rambam and therefore according to Hillel the takkanah to eat marror nowadays is patterned after it was done in the mikdash and therefore the obligation of marror would carry with it another obligation of eating matzah. Says the P.M., this is the basis for the opinion of the Taz that eating korach is part of the mitzvah of eating maror and not a mere zecher liMikdash.
The opinion of Tosfos is that both according to the Rabbanan and Hillel one can fulfill the mitzvah of matzah and maror whether eaten separately or in a sandwich, the machlokes is only which way is better to do. Being that this is the case, the Pri Migadim's explanation is problematic, for Tosfos says even without the korech the mitzvah is fulfilled according to Hillel, so since we eat matzah and maror each independently before korech, the korech is no longer needed for the mitzvah? In addition, the Ran takes issue with Tosfos for if in his view one can be yotzei the mitzvot independently according to Hillel, why would there be a takkanah to do them together if Hillel agrees even in the times of the Mikdash one already fulfilled their obligation?
Rabbi Ezra Shochet (Ohalay Torah journal volume 917) suggests that there are two laws according to Hillel (in the view of Tosfos) for fulfilling maror. There is an obligation to eat matzah and maror each independently and that point is agreed by all. The machlokes between Hillel and the Rabbanan is if there is an additional mitzvah of כריכה. So when Tosfos says that one can fulfill maror without korech he means the mitzvah of maror but there would not be a fulfillment of them mitzvah of כריכה. It is that kium which we are obtaining by eating matah and maror together. In other words, we are not eating matzah again to fulfill the optimal mitzvah of korech, we are doing it to fulfill the mitzvah of having a כורך and that we do as a zecher to the Bibical mitzvah of having maror in a כורך.
The opinion of the Ramban (Milchamos,) Chidushay HaRan etc. is that according to Hillel one can not fulfill the mitzvah of maror without a korech. It should follow then that according to Hillel there is no way to fulfill maror nowadays since one can't eat it with the matzah which has a Torah obligation and if one already ate matzah, then there is no obligation at all to eat matzah. So, they explain we eat כרוך as a זכר למקדש. In other words, according to Hillel we would have a takkanah to eat matzah and marror as a זכר למקדש. They could have said like the Pri Migadim suggested that the Rabbanan would give an obligation to eat matzah in a korech in order to fulfill matzah properly. Why do they not say that? Rav Shochet suggests that they hold like the opinion of Rashi that according to Hillel the pesach is part of the sandwich and since that is impossible and the kricha will not be fulfilled anyway, there is no point is making a takkanah to eat maror and matzah in a kricha and are forced to say we only eat it as a זכר למקדש. This would be the approach of the Bach. What is unclear to me is that in the world of Hillel the Rishonim say we would do the maror together with matzah. In other words, there would be a takkanah to eat the matzah together with the maror as the zecher liMikdash even though it is an incomplete mitzvah. So, why would we not say the same thing for us that do like Hillel and say that we do matzah with maror as a takkanah of zecher limikdash? In other words, not like the Bach that we eat korech as a zecher to past times, but there is a takkanah of doing the mitzvah of maror zecher liMikdash just like we say according to Hillel? As will be explained in essence that is the approach of R' Braun in the Alter Rebbe.
The Alter Rebbe paskens (475:16) like Rashi that the korech of Hillel is pesach, matzah and maror. However, in the next halacha he says that according to Hillel we eat korech in order to fulfill the obligation of maror. (That's why he says in sif 18 the beracha of matzah and maror also goes on the korech and one should not speak in the middle.) What is the point of doing korech with just matzah and maror if that doesn't fulfill the mitzvah of maror anyway since it is not being eaten with the pesach? In other words, how can the Alter Rebbe say like Tosfos that we ate korech to fulfill the mitzvah according to Hillel (whether that means the mitzvah of kricha or the mitzvah of maror,) if that can't be fulfilled anyway since there is no korban Pesach? He should say we eat the korech only as zecher liMikdash like the Ramban and Ran? And why does he say the beracha of matzah also goes on the korech, the korech is only done to fulfill the mitzvah of maror, what does it have to do with them matzah?
Rabbi Shochet suggests that the Alter Rebbe holds there is an independent mitzvah of korech and that is only fulfilled with all three items of koran pesach, matzah and maror together. However, he holds that what Tosfos writes is true even according to Rashi that the mitzvah is all three because the mitzvah of maror is said to be done in a kricha (according to Hillel.) So, therefore we are fulfilling the mitzvah of maror which is to be done is a kricha when we do korech. In order to fulfill this law, there is a takkanah to eat matzah again in order to be able to fulfill the kricha.
Rabbi Yeshayu Braun is not happy with this idea that there is a din in maror that it must be eaten in a kricha irrespective of the general law of everything being eaten in a kricha according to Hillel. He says the peshat in the Alter Rebbe is that the entire mitzah of maror, the Alter Rebe says in sif 15 is a זכר למקדש. In other words, the maror we eat is not a takkanah to remember the bitterness of slavery but to fulfill the mitzah as was done in the Mikdash. Hence, we are faced with a problem according to Hillel for that is impossible since there is no korban Pesach? Therefore, the Chachamam had to make a taakkanah to do a kricha which is the mostly closely patterned after how it was done in the Mikdash in order to be able to fulfill the "maror of the Mikdash." For this takkanah it was necessary to make an obligation of matzah and maror to be eaten together. In other words, donig korech is a takkanah in order to facilitate a מעין of the true fulfillment of maror. With this idea he explains why we say זכר למקדש כהלל, why do we say it, and why does the Alter Rebbe say to say it before eating the korech, why are we not worried about it being a הפסק like the Mishna Berura asks? Since the korech is not actually doing the cheftzah of the mitzvah in the Mikdash since we are lacking the Pesach, in order to acknowledge its function as a זכר למקדש we proclaim our actions are a זכר למקדש and is not considered a הפסק for it is part of creating the זכר למקדש. .
However, in the end, the Taz backs down for the Tur indicates that speaking does not disqualify the korech bidieved. Rabbi Braun wants to say not like R' Schochet that the P.M.'s explanation of Tosfos is standing even in the initial thought process of the Taz and we are forced to explain there is some kium even after eating matzah and maror. Rather, the Pri Migadim is mainly coming to address the conclusion of the Taz in which he agrees the korech comes only as a zacher to what Hillel did. However, even Rabbi Braun is forced to acknowledge that the Pri Migadim's words also came to address the first approach of the Taz that the korech is more than a mere zecher and in that approach the Rabbinic takkanah of korech would be more strict that the true Bibical enactment and it would be מעכב.