Based on: I. Ta-Shma, Early Franco-German Ritual and Custom, Jerusalem: Magnes Press, 1992 [Hebrew].
The following ingredients may be used in fulfilling the obligation to eat matzah: Wheat, barley, spelt, oats, and rye. But not rice or other types of legumes. Nor are they capable of leavening, so it is permissible to use them in cooking.
Gloss by R' Moses Isserles: And there are some who prohibit them. And the custom in Ashkenaz is to be stringent, and one sould not change this...
And concerning legumes like peas, beans, rice, lentils and the like, our rabbis are accustomed to prohibit eating on Passover altogether, and this seems correct.
I believe that I have heard that one should only cook beans on Passover in water that is boiling from the moment they are placed in the pot. However, prominent authorities are permissive about this.
My teacher R' Jehiel was in the habit of eating the light bean called pois on Passover, and he used to claim this in the name of prominent authorities.
As proof for his position he noted that even with respect to rice, which Rabbi Johanan ben Nuri treated as a form of grain with respect to leavening, the Talmud declared that nobody takes Rabbi Johanan's position into account.
Nevertheless, it is very difficult to permit something that has been universally treated as forbidden since the days of the early sages. Presumably they did not forbid it on account of actual leavening, since they would not have erred on a matter that would be obvious to any schoolchild who has studied some Halakhah; since it stated explicitly in Pesahim that only the five designated species are subject to leavening.
For this reason it seems preferable to uphold the custom and forbid all kinds of legumes on Passover, not out of concern for actual leavening (for it would be a gross error to say that), but as a precautionary prohibition; i.e.,since both legumes and grains are cooked foods... there is a danger of confusing the two... And even though the Talmud permits rice, that applied only in their days when everyone was knowledgeable in the laws of what is prohibited and what is permitted. However now, in recent generations, it is obvious that we should make the precautionarty prohibition.
Mishnah: The following ingredients may be used in fulfilling the obligation to eat matzah: Wheat, barley, spelt, oats, and rye...
Talmud: Only these, but not rice or millet.
Whence do we know this -- Said R' Simeon b. Lakish, and thus the School of R' Ishmael taught, and thus the school of R' Eliezer b. Jacob taught, Scripture says, "Thou shalt eat no leavened bread with it, seven days shalt thou eat unleavened bread therewith" (Deuteronomy 16, 3): With commodities which come to the state of leaven, a person can discharge one's obligation with unleavened bread made thereof. Accordingly these are excluded, since they do not come to the state of leaven, but rather to the state of decay.
Our Mishnah does not agree with R' Johanan ben Nuri, who maintains: Rice is a species of grain, and kareth [divinely inflicted death penalty] is incurred for [eating it in] its leavened state.
For it was taught: R' Johanan ben Nuri prohibits rice and millet, because it is close to becoming leaven.
The scholars asked: Does "because it is near to becoming leaven" mean that it quickly becomes leaven, or perhaps that it is near to leaven, but is not completely leaven?
Come and hear: For it was taught, R' Johanan ben Nuri said: Rice is a species of grain and kareth is incurred for [eating it in] its leavened state, and a person fulfills the obligation with it on Passover. And thus R' Johanan ben Nuri used to say, Karmith [cow-wheat] is subject to hallah.
...And similarly with respect to legumes, it is customary to act stringently, to avoid eating them unless they were cooked in boiling water.
I subsequently heard that my teacher R' Judah [of Paris] would eat them himself, and afterwards many tended to act leniently. God forbid, that no mishap resulted from their actions!
And in the She'iltot of Rav Ahai I found written at the end of the Laws of Passover: "All types of legumes may be cooked whether on Passover or on other festivals."
And furthermore, R' Moses Maimonides wrote in his book (Hilkhot Hametz Umatzah 5:1) that even if they are soaked in water all day, they will not rise, since they are not susceptible to leavening, only to decay.
Even though I found these arguments persuasive, and our ancestral custom is based on an error, and it does not fall into the category of practices that are permitted [but are prohibited by others; where one should act stringently], they should not be treated leniently out of consideration for those who prohibit them.
It is written in Sefer Ha-Minhagot: It is the widespread custom not to eat pulse on Passover because they are subject to leavening, and for this reason they are referred to as himtzi. It seems unreasonable to suggest that this custom would be based on any prohibition whatsoever, since no legume in the world is capable of leavening.
Rather, it is because there is no real need to eat legumes on the festival, seeing that it is written "And you shall rejoice in your feast" (Deuteronomy 16:14), and there is no joy in bean dishes.
Undoubtedly, if a person wanted to eat pulse on Passover, or something similar made from other types of legumes, then it would be permitted, and there is not the slightest suspicion of prohibition; notwithstanding the prevailing custom, since we state in the Jerusalem Talmud... "Anything that is permitted, though one erroneously prohibits it, can be permitted through consultation [with a sage]."
Any cooking of dough or grain of the five types is forbidden on account of leavening on Passover. However, on other festivals it is permitted to prepare all kinds of dough and all kinds of grain, with the exception of for tisna (barley-groats); i.e., one should not pound it with a large mortar, though it is permitted with a small mortar. All types of legumes are allowed on Passover and on festivals.