Grate cheese. Spread the brown bread with mustard. Cover 2 slices with ham and half the cheese. Place the remaining slices upside down on top. Fry in 2 tablespoons of hot oil on each side for about 5 minutes until golden brown.
Line a baking tray with baking paper. Mix crème fraîche and the rest of the cheese. Put the breads on the baking tray and spread the crème fraiche on top. Bake under the grill for about 5 minutes. Fry the eggs in 1 tsp. hot oil until they become fried eggs, season with salt and pepper.
Place on the loaves of bread and serve.