Wash the zucchini flowers very gently under cold running water. Eliminate the hard pistil from inside and arrange the flowers on a clean tea towel to dry.
Blend the ricotta cheese with the goat cheese in a bowl to obtain a smooth, soft cream. Season to taste with salt, freshly ground black pepper, and parsley.
Open the flower petals and start to fill the inner cavity with the stuffing, taking care not to overdo the quantity. A pastry bag or zip lock bag works best. Close the tips of the petals inwards so that the filling remains in place. Place in the refrigerator for a few minutes while preparing the batter.
Lightly beat the eggs and add in milk, flour, cheese, and parsley. Mix well. Egg mixture should be about pancake mix thickness. If the mix is too thick, the egg coating will be too thick, and if it's too thin, it will run off.
Heat a large sauté pan and then add about ¼ inch of cooking oil to the pan. Dredge zucchini flower in egg mixture, shed any excess egg, and place into hot oil. Continue the process until you fill the pan. Fry each side of the flower until golden brown, about two minutes on each side. The second side may cook faster so keep an eye on them. Place finished blossom on paper towels to drain off any excess oil.
Place blossoms on a serving tray and season with grated Parmesan cheese, salt and pepper. Serve immediately.
Zucchini flowers are very fragile. They are extremely perishable; use the same day.