Remove stamens from squash blossoms. Trim stems to about 2 inches.
For filling, in a medium bowl combine the mozzarella (or other melting cheese), mayonnaise, basil, Parmesan, oregano, garlic powder, and crushed red pepper (if using). In a shallow dish combine flour, salt, and black pepper. In small bowl whisk together egg and milk.
Stuff each blossom with a heaping tablespoon of the filling, lightly squeezing flower together to enclose filling. Working with one at a time, brush blossoms with egg mixture, then transfer to flour mixture, turning and pressing to coat. Transfer to a waxed paper-lined tray. Sprinkle coated blossoms with remaining flour mixture. Chill, loosely covered, at least 30 minutes or up to 4 hours.
In a large skillet add ¼ inch vegetable oil. Heat until very hot and shimmering. Working in 2 batches, fry blossoms in oil, turning once or twice, until golden on all sides. Transfer to a paper towel lined plate. Sprinkle with salt to taste, and additional parmesan and fresh basil. Serve with marinara sauce.