2 tablespoons (1/4 stick) butter
1 pound mushrooms, sliced
3 garlic cloves, minced
2 8-ounce packages frozen artichoke hearts, thawed, coarsely chopped
1 cup dry vermouth
4 1/2 tablespoons butter
4 1/2 tablespoons all purpose flour
4 1/2 cups whole milk
2 1/2 cups freshly grated Parmesan cheese (about 7 1/2 ounces)
1 9-ounce package oven-ready (no-boil) lasagna noodles
1 pound whole-milk mozzarella cheese, thinly sliced
1. For filling: Melt butter in large skillet over medium-high heat. Add mushrooms and garlic; saute until mushrooms release juices and begin to brown, about 7 minutes. Add artichokes and vermouth. Cook until liquid is absorbed, stirring occasionally, about 10 minutes. Season with salt and pepper.
2. For bechamel sauce: Melt butter in heavy medium saucepan over medium-high heat. Add flour; stir 1 minute. Gradually whisk in milk. Reduce heat to medium and simmer until sauce thickens and lightly coats spoon, stirring occasionally, about 20 minutes. Stir in 1 1/2 cups Parmesan. Season to taste with salt, pepper, and ground nutmeg.
3. Spread 2/3 cup béchamel sauce over bottom of 13x9x2-inch glass baking dish. Top with enough noodles to cover bottom of dish. Spread 1/4 of artichoke mixture over. Spoon 2/3 cup béchamel sauce over. Top béchamel with 1/4 of mozzarella.
4. Sprinkle with 3 tablespoons Parmesan. Top with enough noodles to cover. Repeat layering 3 more times, finishing with a layer of noodles, then remaining béchamel. Sprinkle with remaining Parmesan. (Can be prepared 1 day ahead. Cover with foil and refrigerate.)
5. Preheat oven to 350 F. Bake lasagna covered with foil 1 hour (or 1 hour 15 minutes if chilled). Remove foil. Increase temperature to 450 F. Bake lasagna until golden on top, about 10 minutes longer.