my utility function is basically whatever I want it to be.

If utility functions are those constructed by the VNM theorem, your utility function is your wants; it is not something you can have wants about. There is nothing in the machinery of the theorem that allows for a utility function to talk about itself, to have wants about wants. Utility functions and the lotteries that they evaluate belong to different worlds.

Are there theorems about the existence and construction of self-inspecting utility functions?