Creamy Brussels Sprout and Mushroom Lasagna Recipe

Name: Creamy Brussels Sprout and Mushroom Lasagna Recipe
Ingredients: 1 package (15 sheets) no-boil lasagna noodles; 24 ounces button mushrooms, cleaned and trimmed; 1 pound Brussels sprouts; 5 tablespoons unsalted butter, divided; 2 medium shallots, finely chopped (about 1/2 cup); 4 medium garlic cloves, minced (about 4 teaspoons); 1 tablespoon picked fresh thyme leaves; 2 cups heavy cream (divided); Kosher salt and freshly ground black pepper; 2 tablespoons canola oil; 3 tablespoons flour; 3 cups whole milk; 1/4 teaspoon grated nutmeg; 1 pound whole milk mozzarella cheese, grated, divided; 1 ounce grated Parmiggiano-reggiano; 2 tablespoons chopped fresh parsley leaves