Now, this is very much not my style, but just because I feel like "getting it out there" I'll share some secrets here.
[Now, this is not for those Ashkenazim who are stringent on themselves, to not eat Matzah that came in contact with water or any other liquid (though I think that opinion has a thin halakhic basis).]
Hold two matzot under water, make a ground beef sandwich between them, cut it into four pieces, dip both sides in egg, and that fry that mother f---er (oh, and the meat obviously has to be cooked before hand. Fry under a low flame).
I recently experimented with this recipe to make it an egg sandwich and a grated carrot sandwich (I have vegan leanings). ..they were essentially flops though, but I still think the idea is a good one).