Heat your oven to 375°F.
Bring a large pot of water to boil with salt and a splash of oil. Add the lasagna noodles and cook for 10 minutes. Drain and set aside.
Bring the milk and garlic to simmer in a saucepan, or heat it in your microwave, and set it aside.
Melt ½ cup (8 tablespoons or 115 grams) butter in a large saucepan. Add the flour and cook for one minute over low heat, stirring constantly. Pour in the hot milk gradually, stirring until combined. Add salt, pepper, and nutmeg. Cook over medium-low heat, stirring frequently, for 3 to 5 minutes, or until thick. Set aside.
Slice mushrooms ¼-inch thick. Heat 2 tablespoons olive oil and 2 tablespoons butter in the pot used to cook the noodles. Cook half the mushrooms with a couple pinches of salt for about 5 minutes, or until tender. Repeat with remaining mushrooms.
Spread some of the sauce in the bottom of an 8 x 12 or 9 x 13 baking dish. Arrange a layer of noodles on top, then more sauce, ⅓ of the mushrooms, and ¼ cup grated parmesan. Repeat two more times, then top with a final layer of noodles, remaining sauce, and last ¼ cup of parmesan.
Bake for 45 minutes, or until top is browned and the sauce is bubbly. Let sit at room temperature for 15 minutes before serving. To freeze, allow to cool completely and wrap in plastic wrap before freezing.
