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1. Soften noodles in a pan of very hot water while you prep the other ingredients. 2. Make bechamel (white sauce): Bring milk to a simmer in a saucepan and remove from heat. Melt butter in a large saucepan over medium heat. Add flour and cook, stirring, until slightly darkened, 2 minutes. Whisk milk into flour mixture all at once and whisk until smooth. Add 1 1/2 tsp. salt, 1/2 tsp. pepper, and the nutmeg. Sauce should be thick enough to coat a spoon; if it isn't, cook over medium-low heat, stirring, until thickened, 2 to 3 minutes. Remove from heat and stir in garlic, 2 tbsp. parsley, and 1/2 tbsp. thyme. Keep covered. 3. Preheat oven to 375u00b0. Heat a deep, wide pot over medium-high heat 2 minutes. Swirl in 1 tbsp. oil and add leeks. Cook until tender but not browned, 3 to 4 minutes, stirring occasionally. Scoop leeks into a bowl and set aside. 4. Swirl 2 tbsp. oil into pot. Add mushrooms, season lightly with salt and pepper, and cook over medium heat, covered, until mushrooms are tender and beginning to release juices, about 5 minutes. Uncover and cook until edges start to brown. Stir in leeks and remaining 1/2 tbsp. thyme. Remove from heat. 5. Mix parmesan with asiago. 6. Assemble lasagna: Oil a 9- by 13-in. baking dish. Spread a few spoonfuls of bechamel over bottom. Arrange 3 noodles crosswise in dish, then spoon on about 1/2 cup bechamel, followed by a third of the mushrooms and 1/3 cup cheeses. Repeat layers twice more. Top with a final layer of noodles and bechamel, and sprinkle with remaining cheese. 7. Bake lasagna until browned and bubbling, about 45 minutes. Sprinkle with remaining 1 tbsp. parsley and let sit at least 15 minutes before slicing.
