Whisk egg and milk. Season well with salt and pepper. Cut mozzarella into 8 slices. Wash the basil, dab dry and pluck the leaves from the stalks. Place slices of bread next to each other on a deep plate and pour the egg milk over them.
Leave to stand until the liquid has been absorbed. Turn the bread once in between. Cover four slices of bread with two mozzarella slices each. Spread basil on top, sprinkle with pepper and cover with the remaining 4 slices of bread.
Press the edges of the bread slices firmly together. Heat the oil in a large frying pan, carefully slide in the slices of bread and fry them over medium heat until crispy on both sides. Remove the bread from the pan and let it drain well on kitchen paper.
Arrange one bread halved on each plate. Serve garnished with basil and tomato and sprinkled with pepper.