Heat olive oil in a large Dutch oven over medium-high heat. Add onion, celery, carrots, garlic and chili flakes; cook until fragrant and softened, about 5 minutes.
Add the butter and stir in the orzo. Sauté until golden; 1 to 3 minutes.
Pour in the broth, Italian seasoning, and bay leaf. Add shredded chicken. Bring to a boil over high heat. Season with salt and pepper to taste. Simmer for 8 to 10 minutes or until the orzo is al dente, stirring frequently.
Stir in the milk, spinach and lemon. Cook until few minutes or until the greens are wilted and the soup is warmed through.
Divide the soup among bowls and top with Parmesan, black pepper, and fresh parsley.
