Non native english speaker here, not trying to have an argument but to learn.
Is it correct to use "whose" in this context?
I kinda thought "whose" was meant to refer to a person and not an object, but really I don't know.
Though I'd use something like "of which" or whatever else instead.
(Or just do what I do and rephrase it so you don't need to bother with this syntax to begin with.)
"What is a dish where each individual component you like, but when combined together become a dish you think is nasty?"