Slice the mozzarella and divide among 4 slices of bread. Top with the remaining 4 slices of bread.
Whisk the eggs with the milk in a small casserole dish and sprinkle with salt and pepper.
Add the flour to a casserole dish. Dust the sandwiches in the flour, and then dip into the egg mixture.
Heat about 3 tablespoons olive oil in a large nonstick pan. Add the sandwiches to the pan and fry on both sizes until golden and crisp, about 10 minutes. The mozzarella should be completely melted and very "stringy" when the sandwich is eaten. Slice the sandwiches in half to make 2 triangles.