What kind of critter..

[ChrisR]

Produces a web, but also "maggots", and also eats its way out of a sponge cake covered in chocolate?

One such crawled its way out to alarm one of my 12 year-old electronics students. She had taken a bite. And yes, she squealed.

Rice-grain looking Maggot is lost unfortunately, but the exit hole is clear, as is the stringy web.

A likely suspect:
https://en.wikipedia.org/wiki/Indian_mealmoth