Preheat oven to 400 degrees F.
In a saucepan, melt the butter for the bechamel, and add the flour, stirring gently to make a smooth paste. Remove the pan from the heat and whisk in the milk. Turn the heat back on to medium, and stir the bechamel until it begins to thicken and come to the boil. Let it bubble for about 5 minutes to get rid of the floury taste. Take off the heat and season with salt, pepper, and nutmeg.
Melt 2 tablespoons butter and the oil in a large wide pan. Drain the porcini, reserving the liquid, and chop before adding to the pan with 3/4 cup chopped parsley, the dried or fresh thyme, and garlic. Stir for a couple of minutes then melt the remaining 1 stick of butter in the same pan and add the chopped mushrooms, stirring for about 5 minutes. The mushrooms will appear dry at first but will eventually start to give off some liquid.
Add the porcini soaking liquid, which the mushrooms will largely absorb, but keep stirring and add the sherry and let it bubble away. Turn off the heat when you have a bronzed, syrupy stew.
Stir the mushroom mixture into the bechamel and add 1 cup of the Parmesan and the other 3/4 cup of the chopped parsley. Put a big pan of water on for the pasta, and when it boils, salt it well. Cook the pasta until al dente, then drain and add to the mushroomy white sauce, stirring it as best you can to get the pasta covered.
Turn into the large roasting pan and sprinkle over the remaining 1 cup of Parmesan. Bake for 30 minutes or until the top begins to turn golden in places.
When the tin comes out of the oven, decorate with the remaining 1/4 cup chopped parsley and some sprigs of fresh thyme.