Creamy White Lasagna Soup

Name: Creamy White Lasagna Soup
Ingredients: 1 medium yellow onion; 8 ounces white button or cremini mushrooms; 3 cloves garlic; 2 ounces Parmesan cheese (about 1 cup freshly grated or scant 1/2 cup store-bought grated); 4 ounces low-moisture mozzarella cheese; 4 tablespoons (1/2 stick) unsalted butter; 1 1/2 teaspoons kosher salt, divided, plus more as needed; 1 teaspoon dried Italian seasoning; 1/4 teaspoon freshly ground black pepper, plus more for serving; 1 to 1 1/2 pounds boneless, skinless chicken breasts; 2 tablespoons all-purpose flour; 1 (32-ounce) carton low-sodium chicken broth (about 4 scant cups); 1 cup water; 8 ounces dried lasagna noodles (about 8 sheets); 2 cups baby spinach (2 ounces); 1/4 cup heavy cream; 1/2 cup ricotta cheese