Preheat the oven to 375 degrees F.
In a large, heavy saucepan, melt 4 tablespoons of the butter over medium-low heat. Add the onion and cook until it softens; add the mushrooms and raise the heat slightly to cook them through. Sprinkle the onion and mushrooms with flour, stir for a few minutes to cook out the flavor of the flour, add the dried porcini to the pot, and remove from the heat. Stir in the broth with a wooden spoon and keep stirring to break up any floury lumps and make a smoothish sauce. Stir in the milk and return to the stove.
Cook the sauce over medium-high heat, stirring, for about 7 to 10 minutes, or until it thickens. If there are any floury lumps, whisk the sauce briefly with a wire whisk. Remove from the heat and season with the nutmeg and salt and pepper. Set the sauce aside.
Cook the pasta in a large pot of rapidly boiling salted water until it is just not quite al dente, as it will cook further in the oven, and drain.
In a buttered large shallow pan or baking dish, in layers add a quarter of the sauce, a quarter of the cheese, and a third of the tuna, peas, and noodles. Repeat layers two more times, and then end with a layer of sauce and a layer of cheese. Sprinkle with the parsley and crumbs, then dot with the remaining tablespoon of butter.
Bake until bubbly, lightly browned, and crisped in spots, about 30 minutes. Serve immediately.