Chicken Alfredo Lasagna

Name: Chicken Alfredo Lasagna
Ingredients: 1 large chicken breast or 2 small chicken breasts (see Cook's Note); 1 teaspoon Italian seasoning; 1/2 teaspoon kosher salt; Freshly ground black pepper; 1 tablespoon olive oil; 6 tablespoons unsalted butter; 6 cloves garlic, minced; 2 tablespoons all-purpose flour; 2 cups milk; 1 cup heavy cream; 1/4 teaspoon grated nutmeg; Kosher salt and freshly ground black pepper; 3 cups shredded Parmesan; 9 oven-ready lasagna noodles; 1/2 cup chopped fresh parsley, plus additional for garnish; 12 ounces shredded mozzarella