Pesachim 37 - Cookies baked by Baitus
The Sages taught, "One cannot bake ‘thick bread’ on Passover - so says Beit Shammai, but Beit Hillel allows it." What could this mean? If it means bread one hand-breadth thick, like they used to bake in the Temple, without giving it a chance to leaven - then how can Beit Hillel allow it? Obviously, priests in the Temple could be trusted to use dry wood, hot metal ovens, etc., but not the general populace. Rather, this particular rule is just talking about abundant bread, and Beit Shammai forbid it simply because it is too much work for a holiday. If so, it should be applicable to all holidays! - You are right, it is, just that our teacher was teaching it on Passover, so he used the Passover name.
In general, matzah should be baked quickly, so that the dough does not get a chance to rise and become chametz. What about special cookie-formed dough for the matzah? A baker by the name of Baitus sought a permission to bake such matzot, since he was doing it very fast. However, the Sages asked him, "What will the people say? That all cookie-matzot are forbidden, but that of Baitus are allowed?" Certainly, a non-professional baker cannot do it fast enough, and for her it is forbidden.
Some reverse this logic: a home-based baker does quick, simple cookie-matzot, and for her it is allowed. However, a baker is going for fancy ones, it takes him more time, and is therefore forbidden.
Art: The Pancake Baker by (after) Gabriel Metsu