Technically this would be known is tomato pie.
Is "Pizza with no cheese?" wrong?
It's correct! Accepted today.
What's the rule on which nouns take the -у in genitive and which nouns take the -а?
Neuter nouns take endings -a, -я.
Due to historical changes masculine nouns take two sets of endings in Genitive case: -а, -я (countable or concrete objects) or -у, -ю (materials, substances and abstract nouns).
and "хліб" is an exception, it takes an -а at the end.
Those historical changes are Polish. Polish has the same grammar rules on -a/-u masculine noun genitive case.
Maybe I can't say about Polish, but I'm sure about Ukrainian.
I'm the weirdo who always order pizza without cheese. lol
I do not hear "p" there is only "izza"
I easily hear the "п" in "піца"