Really? I think you can only say "such a bowl" or "such bowls" (which is not in the sentence), but not "such bowl".
Just an opinion of a native that I ask such questions, I'm afraid. Fluent in both American and British English.
I think it's because "such" isn't a determiner. The sentence "Do you have such bowl?" is incorrect because "Do you have bowl?" is incorrect. Meanwhile, the sentence "Do you have such bowls?" and "Do you have such a bowl?" are correct because "Do you have bowls?" and "Do you have a bowl?" are correct.
A dish or a bowl, they both mean essentially the same thing, and both are countable nouns.