Translation:My grandmother has cooked something tasty.
It doesn't work like that. Consider the sentence: "Вчора моя бабуся приготувала щось смачне" – perfectly valid in Ukrainian (based on my Russian knowledge, if it's invalid in Ukrainian specifically I'd like a reference/explanation, it would be very interesting!). However, in English you can't say "Yesterday my grandmother has prepared something tasty".
On the other hand, if you say "Вчора моя бабуся готувала щось смачне", it would translate into the progressive tense: "Yesterday my grandmother was preparing something tasty".
Can you please explain me why you can not say: for example : I have prepared something to eat. / I have cooked something. / I have made a tasty juice..etc. ( per your explanation I can not also use these sentences, huh? What is wrong with these sentences? However, why are you talking about "yesterday" ? You have to distinguish "past tense" and " past perfect tense". don't mix them.
Ynhockey is right. Ukrainian does not have separate tenses that match one-to-one to the English Present Perfect and Past Simple tenses. Therefore, the given Ukrainian sentence can be translated using both Present Perfect and Past Simple. It will depend on the context which one to use.