The past conjugation of 'to eat- essen'
The usage of "was aßt du" (what did you eat) is really not common in Germany, nobody says that. "Was hast du gegessen" is used instead.
Imho it does not need to be taught. It is an illegit abbreviation of "aßest" where the schwa sound was neglected in pronunciation. It does not meet the usual conjugation paradigms, but its coming into being is simply due to misunderstanding and bad pronunciation. It is simply due to lack of grammatical knowledge that this form even exists in several books as a variant of "aßest" (which would be regular). Plus, you will never ever encounter that except for in broken speech. I would not consider that sufficient...
I would go for "Was aßest Du". The other one ("Was aßt Du") is a bit odd and does not even meet the standard conjugation paradigms. Even though "Was aßt Du" is reckoned okay with several sources, it makes my ears hurt. Really hurt. I will always deem it ungrammatical (and if there are more speakers who have a similar feeling, it might be a bad option indeed. I would strongly advise against its use).
I have come across "Was aßest Du" (and "Was aßt Ihr"), but have never ever heard "Was aßt Du".