What are the halachic or minhag issues in eating matza with spreads like cream cheese?
Many people have written in various posts that they keep gebrochts and put, for example, cream cheese on matza.
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The famous source of Gebroks is from the Shu"t of R' Shneur Zalman of Liadi (Siman 6) where he says "ובמי פירות פשיטא דאין להחמיר כלל כל הפסח" (One doesn't have to be strict [not to dip Matza in] fruit juice during Pesach).
The simple reason is that it says in his Shulchan Aruch:
וכל המשקין שבעולם שאינן מתולדות המים שיתבאר בסי' תס"ו הם נקראים מי פירות כגון היין ושמרי היין והשמן ומי תותים ורימונים ושאר כל הפירות ואפילו משקין שאינם באים מפירות כגון החלב והדבש ומי ביצים וכיוצא בהם הם בכלל מי פירות לענין זה ואפילו משקים חמוצים כגון מי תפוחים חמוצים וכיוצא בהם אם לש בהן עיסה אע"פ שנתחמצה מהם מותרת שאין זה חמץ שאסרה תורה:
All liquids in the world that aren't "descendants" of water like:
- Berry juice
- Pomegranate and other fruits.
Moreover, even liquids which don't come from fruits like 5. Milk 6. Honey 7. Egg water
qualify as fruit juice for this matter. If one kneaded dough with these liquids, even if it rises, it's permitted since this isn't the Chometz which the Torah forbids.
(However, this is only true when, as it says in the next syif, these are pure. However, if water gets mixed in that water makes the dough truly Chametz).
As a result, the Rebbe Rashab wouldn't eat Matza with meat or fish but would eat it with (guarded) wine or milk (see the next page there).
However, the Previous Lubavitcher Rebbe was reported as eating Matza separate from the meal and (to the best of my knowledge) the Rebbe didn't mix Matza with anything.
So while there is a place to say that one is allowed to eat "pure" cream cheese (if the Hashgacha will guarantee that no drop of water was mixed in, the factory was dried, etc.) it seems to be fairly rare to find such a product.
There are those who are extremely careful about Gebrokts, to the point where they won't have Matzah and liquids on the table at the same time/eat the Matzah over a separate bag, etc. to ensure that there is no way any liquid could reach the Matzah.
There are many others who aren't that extreme, yet still don't eat Gebrokts. As the "worry" of Gebrokts is that you might cause some flour to become Chametz, the issue would only occur if the liquid is applied to the Matzah and given time to "rise". So with your example of Cream Cheese, it wouldn't be an issue to spread it on the Matzah right before eating (maybe not on the whole Matzah at once, if you're a slow eater like me ;) ), however, Gebrokts keepers probably wouldn't spread Cream Cheese on their Matzah in the morning and save it for lunch.
Source: Personal experience as a life-long member of a non-Gebrokts eating family (seriously everybody, it's not that bad). Yes, I know that isn't the best of sources, but it's what I've got.