In a shallow bowl, combine 3/4 cup of cheese, eggs, 2 tablespoons flour, parsley, salt, pepper, garlic and milk; whisk or beat until smooth; cover and refrigerate for at least 15 minutes.
Cut zucchini in half cross-wise, then into lengthwise slices about 1/4 inch thick; lightly dust each piece with flour.
Heat about 1/4 cup of vegetable oil in a wide frying pan over medium heat; using a fork, dip each zucchini slice into cheese mixture, thickly coating both sides; place in pan, a few pieces at a time, and cook, turning once, until golden brown on both sides.
Drain briefly on paper towels, then transfer to a serving plate and keep warm until all are cooked (add additional oil to pan as needed).
Sprinkle to taste with additional cheese and serve.