Combine the eggs and milk in a bowl and season lightly with salt and pepper. Put the flour in a separate bowl.
Divide the mozzarella slices between 4 bread slices and top each with 3 basil leaves. Lay a second bread slice on top of each to make 4 sandwiches. Press down firmly on each sandwich with the heel of your hand, then cut off and discard the crusts.
Heat half the oil in a large frying pan over a medium heat. Turn 2 of the sandwiches, 1 at a time, briefly in the flour to give a light coating, then dip in the egg mixture, making sure that they are well covered. Add to the pan and cook for 3–4 minutes on each side until golden and crisp. Remove and keep warm in a low oven while you cook the second batch of sandwiches in the remaining oil. Serve with a few lettuce leaves, if liked.