Preheat the oven to 180 degrees (convection: 160 degrees). Toast the bread slices. Brush with 1/2 tbsp butter each and top with 1 slice of ham. Scatter 1 tablespoon each of grated cheese on top and bake the toasts in the oven for about 3 minutes.
Wash the chives, pat dry and cut into rolls. Heat the oil in a pan and fry 4 fried eggs, season with salt and pepper.
Take the toasts out of the oven, cover with 1 fried egg and serve sprinkled with chives.