Have fun preparing this mushroom dish!
Heat the milk and butter in a small pan until the butter is melted. Chill slightly.
Mix eggs in a baking bowl. Pour in the milk. Add flour and salt and mix until smooth. Allow to swell for at least fifteen minutes.
In the meantime, for the filling, prepare mushrooms (prepare ready to cook, e.g. peel, remove woody parts and dirt) and cut into thin slices. Sauté in half the butter, the mushrooms draw juice, evaporate it completely. Set aside.
Remove the skin from the shallot and chop finely. Sauté in the remaining butter until light yellow. Sprinkle the flour over it and steam briefly. Slowly add the milk and bring to a boil. Make the sauce on low fire for five minutes. Then add the crème fraîche and 3/4 of the cheese. Season with salt, pepper and a pinch of nutmeg.
In a non-stick frying pan, fry the dough in a little butter, one after the other, in large omelets. Top each omelet with a slice of ham and spread the sauce on top. Sprinkle a good half of the mushrooms on top. Roll up the omelets and place them in a buttered baking dish. Sprinkle with the remaining mushrooms and cheese and drizzle with cream. Meanwhile, bake the omelettes in the oven heated to 200 °C on the second rack from the bottom for about 15 minutes.