Marsala and Mushroom Pasta Bake

Name: Marsala and Mushroom Pasta Bake
Ingredients: Kosher salt and freshly cracked black pepper; 1 pound cavatappi pasta; 6 tablespoons unsalted butter; 6 cups sliced mixed mushrooms (shiitake and cremini); 1 medium yellow onion, thinly sliced; 2 cloves garlic, minced; 1 tablespoon finely chopped fresh thyme; 1/3 cup all-purpose flour; 1 cup marsala wine; 3 cups vegetable stock; 1 cup whole milk; Freshly grated nutmeg; 1/2 cup finely chopped fresh parsley; 2 cups shredded mozzarella cheese; 1/4 cup freshly grated Parmesan