Melt 1 tablespoon of the butter in a medium skillet. Add the mushrooms and sauté over medium-high heat until tender, about 2 to 3 minutes; remove with a slotted spoon.
Remove excess liquids from the skillet and add the remaining 3 tablespoons of butter; reduce heat to medium. Add the flour to the melted butter and cook for 2 minutes, stirring constantly. Gradually stir the milk into the roux. Cook, stirring constantly until is thick and creamy.
Add the whipping cream, Parmesan cheese, diced ham, and cooked mushrooms to the sauce mixture. Season with salt and pepper to taste. Add the parsley and cook until hot.