Cover 4 slices of bread with ham and cheese. Cover with the remaining 4 slices of bread. Heat 2 tablespoons of butter bit by bit in a pan. Fry the croquettes in it in portions on each side for 2-3 minutes. Keep warm.
In the meantime, heat 1 tablespoon of butter in a second pan. Fry the eggs in it until they are fried. Season with salt and pepper. Spread 1 tablespoon of mayonnaise on each croque. Arrange the fried eggs on top.