Sift together the flour and baking powder. Set aside. In a large bowl, combine the egg, olive oil, 1/2 cup of the milk, salt and pepper.
Beat to a smooth paste and gradually add sifted flour mixture (consistency will be very stiff). Add grated cheese and remaining milk to make a smooth but stiff batter.
Blend in grated zucchini, garlic, onion, and parsley. Heat the cooking oil to the deep-fry stage and drop in the batter by spoonfuls. Fry until golden.
Remove with a slotted spoon and drain on paper towels. Keep warm until all are cooked. Lightly salt to taste and serve immediately.