Pour the milk into a large saucepan and bring to a boil. Slowly whisk in the semolina, stirring constantly. Reduce the heat to medium and cook until the mixture starts to pull away from the sides of the pan, about 10 to 15 minutes. Remove from heat and 1/2 cup butter, 3 tablespoons cheese, the egg, and the prosciutto. Season with nutmeg, salt, and pepper. Mix well.
Pour the semolina mixture out onto a moist work surface, either Formica or marble. Let cool.
Preheat the oven to 375 degrees F. Using butter, grease a 10-inch round baking dish.
Using wet hands, pat the semolina mixture down to 1/2-inch thickness. Cut the semolina into 1 1/2-inch rounds and arrange one layer of rounds across the bottom of the dish. Sprinkle the some of the cheese over the rounds and dot with a little butter. Make a second layer, leaving a 3/4-inch border all the way around. Sprinkle this layer with cheese and dot with butter as before, then make a third and fourth layer, leaving a successively larger border all the way around on each layer, and topping each layer with butter and cheese.
Bake until the top is browned, about 30 minutes. Serve hot, sprinkled with parsley.