Spread the slices of bread with mustard on one side. Cover 2 slices with the ham and half of the cheese. Place the remaining slices on top. Heat 1 tablespoon of oil in a frying pan and fry the sandwiches for about 10 minutes, turning them over.
Mix the crème fraîche and the remaining cheese. Place the sandwiches on a baking tray lined with baking paper and spread the crème fraîche mixture on the bread. Bake under the grill of the oven (approx. 240 °C) for about 5 minutes.
In the meantime heat 1 tablespoon of oil in a frying pan and fry the eggs in it until they are fried. Take the sandwiches out of the oven, place the eggs on top, season with salt and pepper and serve.