Spread slices of bread with butter. Peel garlic and cut into slices. Heat the oil in a large frying pan. Fry ham in it from both sides until crispy. Fry the garlic briefly. Spread the ham and garlic on the slices of bread.
Fry the eggs in the frying fat at low heat until the egg whites have set. Season with salt and pepper. Turn the eggs carefully and immediately cover each with 1 slice of cheese. Cover and fry for another 3 minutes until the cheese begins to melt.
Place cheese eggs on the ham sandwiches.