Can you please tell me what is the food choice / what the food choice is? (inversion)

The inversion has become optional in colloquial English. In the first example you give, there is also a special reason for not inverting: with inversion, a comparatively long and complicated phrase appears in the middle of another constituent. "the food choice for a vegetarian" comes inside "what ... is". Such constructions are difficult to understand and are often avoided in English.

A similar example is "Does that the Moon revolves around the earth at the same rate as it rotates on its axis surprise you?"

Susumu Kuno first studied this phenomenon in English systematically.