A full 2 pounds of mushrooms and plenty of cheese make this lasagna my kind of comfort food! This recipe was inspired by but very different than this recipe from the New York Times.
Cook lasagna noodles according to package directions; drain and set aside, reserving some of the cooking water for loosening up the noodles if necessary.
Heat 2 tablespoons of the olive oil in a large skillet over medium heat. Add leeks; cook and stir until tender. Add mushrooms to leeks; cook and stir until mushrooms are tender but still plump, about 12 minutes. Transfer to medium bowl.
Meanwhile, line a rimmed baking sheet with parchment paper and arrange radicchio on it in a single layer. Drizzle with remaining 2 tablespoons of olive oil and season with Kosher salt and freshly ground black pepper. Bake for 15 minutes, until the edges are lightly browned. Add to mushrooms in bowl and stir to combine. (Leave oven on)
In a medium saucepan, melt butter over medium heat. Add garlic; cook and stir until fragrant. Sprinkle flour over mixture; cook and stir 10 minutes or until lightly brown, take care not to burn the garlic. Whisking constantly, slowly add milk. Continue to whisk until sauce is thick and creamy. Add 1/2 each of the Gruyère and Fontina; stir to combine. Season to taste with Kosher salt and freshly ground black pepper. Pour all but on cup of sauce over mushroom / radicchio mixture and stir to combine.
To assemble lasagna:
Spread reserved cup of sauce across the bottom of a 9x13-inch glass baking dish. Arrange 4 lasagna noodles in a single layer over sauce. Spread 1/2 of mushroom mixture over noodles in an even layer and sprinkle with 1/2 of the remaining Fontina and Gruyère cheeses. Add a second layer of lasagna noodles and top with mozzarella and prosciutto. Add a third layer of pasta and spread with remaining mushroom mixture. Top with final layer of pasta. Sprinkle evenly with remaining cheese, including Parmesan. Cover with a greased sheet of aluminum foil bake for 45 minutes. Remove foil and cook 15 minutes more or until golden and bubbling.