Béchamel: It’s important to cook béchamel long enough to rid it of any raw flour taste. This is one reason you always add cold milk to your roux.

1. Make the béchamel: Place the porcini in a bowl and pour in 1 cup hot water. Let sit for 30 minutes. Drain through a cheesecloth-lined strainer. Squeeze the mushrooms over the strainer to extract the soaking liquid, then rinse well in several changes of water, swishing them around in the water until you no longer see any sand. Squeeze dry, chop coarsely, and set aside. Measure out ¾ cup of the soaking liquid.

2. In a medium saucepan over medium heat, melt the butter and add the flour. Stir together with a wooden spoon until the roux is just barely golden and has a popcorn aroma, 3 to 5 minutes. Add the onion, chile, and bay leaf and continue to cook, stirring, until the onion softens slightly and the raw onion smell is gone. Add ¼ teaspoon salt. The popcorn smell will dissipate and the roux will thicken, then loosen up.

3. Change from the wooden spoon to a whisk and whisk in the milk and the mushroom-soaking liquid all at once. Bring slowly to a simmer, whisking constantly.

4. Turn the heat to low and simmer, stirring very often with a wooden spoon or a heatproof rubber spatula so that nothing sticks to the sides and bottom of the pot. If the flour sticks and scorches, the béchamel will be ruined and you’ll have to begin again. It helps to cook the béchamel in a wide pan you can tip to see the bottom to make sure the sauce is not sticking. Simmer for about 15 minutes, until there is no raw flour taste and the sauce is quite thick.

5. Remove from the heat and press through a sieve immediately, while hot. You can store the béchamel for a few days in the refrigerator. Place a piece of plastic directly over the surface to prevent a skin from forming. When you reheat it, whisk it vigorously.

6. Make the macaroni: Bring a large pot of water to a boil and add a generous tablespoon of salt and the penne. Cook for a minute less than usual. It should be cooked through but a little more al dente or chewy than you’d like it if you were serving it right away. Drain and toss with a tablespoon of olive oil. Set aside.

7. Preheat the oven to 400°F and butter a 2-quart gratin or baking dish. Place the dried morels in a bowl and pour on 1½ cups hot water. Allow to soak for 20 to 30 minutes. Agitate the mushrooms in the soaking water to release more sand, then lift them from the water and let the water sit for a few minutes. Strain into a bowl through a cheesecloth-lined strainer. Rinse the mushrooms, swishing them around in several changes of water to release more sand. Slice lengthwise and set aside with the reconstituted porcini.

8. Heat 1 tablespoon unsalted butter in a wide, heavy saucepan and add the onion and ½ teaspoon salt. Cook gently until tender, about 5 minutes, and add the garlic. Cook for another minute, until the garlic is fragrant, and stir in the reconstituted morels and porcini. Cook, stirring for a minute or two, until the liquid cooks out. Add the fresh mushrooms and ¼ teaspoon salt, and cook, stirring, until the mushrooms are tender and have cooked down somewhat, about 5 minutes. Add the strained soaking liquid from the dried mushrooms and stir together. Bring to a boil and cook until the liquid has reduced by about three quarters, to a thick gravy coating the mushrooms and the bottom of the pan. Rub the thyme between the palms of your hands to release its aroma and stir into the mushrooms along with 1 tablespoon of the parsley: add salt and pepper to taste. Stir in the béchamel and remove from the heat.

9. In a large bowl, toss together the cooked penne, the béchamel and mushrooms, the Gruyère, all but 2 tablespoons of the Parmesan, and the mozzarella. Spoon into the buttered baking dish. Combine the bread crumbs, the remaining Parmesan, and the remaining tablespoon of parsley and sprinkle over the top in an even layer. Dot with the remaining butter.

10. Cover the macaroni with foil and place in the oven. Bake 40 minutes, or until bubbling. Uncover, turn the heat down to 375°F, and bake another 10 to 15 minutes, until the top has browned. Remove from the heat and, once the macaroni has stopped bubbling, serve.