Prosaically is the adverb: in a boring or ordinary way. If someone explains a wild idea prosaically, they tell it with no colour, as if it were a shopping list. If a week passes prosaically, nothing unusual happens. Same slightly bookish tone as prosaic. You will see it more in writing than hear it in the street. Though actually, because prosaic once meant “in prose,” prosaically could once have meant “in ordinary written language, not in poetry.” That older use is rare now. If you meet the word today, it is almost always “in a dull, everyday way.”