Cut 3-inch rounds of bread, using a biscuit cutter. Place a small slice of Mozzarella, cut to fit, on each of half of the bread rounds. Cover with remaining rounds. Press together firmly.

Dip each in flour, then in beaten egg thinned with milk (use 2 tablespoons for 1 beaten egg). Fry as for grilled cheese sandwiches in a mixture of olive oil and butter. Serve hot.