Cut the chicken breasts into servings. Tenderize them just a bit with a wooden mallet. Season with salt and black pepper on both sides. Roll them in the flour, pat them to get rid of the excess and fry them in highly heated butter.
Arrange the braised chicken fillets into a small tray. Bring the cream to a boil on low heat. Add the cheeses which you've mashed with a fork beforehand. Add the grated cheese as well.
Boil the cream and cheeses on low heat until fully melted. Pour the resulting sauce over the chicken fillets and bake in a preheated 356°F (180 °C) oven for 15-20 min.