1. In a pan, sauté the chopped mushroom stems, ham, and shallot with a knob of butter.
2. Once browned, add the flour and stir for 2 minutes. Slowly pour in the milk while stirring continuously with a wooden spoon. Add salt, pepper, and a pinch of nutmeg. Once the mixture thickens, remove from heat and add the cheese. Set aside.
3. Melt another knob of butter in a pan and sauté the mushroom caps for a few minutes.
To finish: Place the mushrooms in a baking dish. Fill with the prepared mixture, top with a small piece of butter, add a spoonful of water to the bottom of the dish, and bake in a preheated oven (180°C) for 25 minutes.