Chicken Alfredo Lasagna Soup

In a large stock pot over medium heat, heat oil. Add onion and celery and cook until slightly softened, 3 to 4 minutes. Add garlic and thyme and cook until fragrant, about 1 minute. Season with chili flakes if using, salt, and pepper. Add butter and stir until melted. Stir in flour and cook until no longer raw, 2 to 3 minutes. Add broth and chicken and bring up to a simmer. Add noodles and cook until chicken is tender and noodles are cooked through, 12 to 14 minutes. Remove chicken and shred, then return to pot.  Add heavy cream, mozzarella, and Parmesan and stir until incorporated, then stir in spinach until wilted. Serve topped with more Parmesan and parsley.