Mushroom-Leek Lasagna

1 pound dried lasagna noodles
4 cups whole milk
12 tablespoons (1 1/2 sticks) unsalted butter, divided
1/2 cup all-purpose flour
1 teaspoon white pepper
1 teaspoon nutmeg

3 tablespoons olive oil

1-3 large leek
1 1/2 pounds mushrooms
1 1/2 cups grated Parmesan
1 1/2 cups Mozzarella, shredded

Prep
Preheat the oven to 375°F.
Wash and slice the mushrooms and leeks to 1/4-inch thick. You may need to wash the leeks again after slicing.

Noodles
Cook lasagna noodles according to the package's instructions. While they are coming, you can begin the sauce and vegetables.
Drain noodles when they are cooked and put cold water in the pot to prevent the noodles from sticking together.

Sauce
Heat the milk to just below a simmer in the microwave; set aside.
Melt 8 tablespoons (1 stick) of the butter in a large saucepan. Add the flour and cook for 1 minute over low heat, stirring constantly with a wooden spoon.
Pour the hot milk into the butter-flour mixture all at once. Add 1 tablespoon salt, the pepper, and nutmeg, and cook over medium-low heat, for 3 to 5 minutes, until thick.

Vegetables
Meanwhile, add 4 Tablespoon butter and the olive oil to a large pan and cook over medium heat until the butter melts. Add the leeks and mushrooms, sprinkle with salt, and cook about 5-10 minutes.

To assemble the lasagna, spread about 1/4 of the sauce in the bottom of an 8-by-12 by 2-inch baking dish. Arrange a layer of noodles on top, then 1/4 of the sauce, then 1/3 of the mushroom-leek mixture, and a heaping 1/4 cup of each grated Parmesan and shredded mozzarella. Repeat 2 more times, layering noodles, sauce, mushroom-leek mixture, and cheeses. Top with a final layer of noodles and sauce, and sprinkle with the remaining cheeses.

Bake the lasagna for 45 to 55 minutes, or until the top is browned and the sauce is bubbly and hot. Allow to sit at room temperature for 15 minutes before slicing; serve hot.

Source: modified from the recipe by Ina Garten.