Cook the Chicken: Heat 1 tbsp olive oil in a large Dutch oven or soup pot over medium-high heat. Add chopped chicken and cook until nearly cooked through, about 4-5 minutes. Remove to a plate and set aside.
Sauté the Vegetables: In the same pot, melt 3 tbsp butter with 2 tbsp olive oil over medium-high heat. Add onions and carrots, and cook, stirring, for 3 minutes. Add green bell pepper and garlic, and cook for 1 minute more.
Thicken the Base: Sprinkle 1/3 cup flour over the vegetables and cook, stirring constantly, for 3 minutes to form a thick roux. Gradually stir in 8 cups chicken broth, whisking to combine.
Add Remaining Ingredients: In a small bowl, whisk 3 tbsp cornstarch with 1 cup additional chicken broth, then stir into the soup. Add the cooked chicken, cannellini beans, chicken bouillon, parsley, basil, oregano, thyme, salt, pepper, bay leaves, and red pepper flakes (if using). Stir in the broken lasagna noodles.
Simmer: Bring the soup to a boil, then reduce to a simmer. Cook, stirring occasionally, for 20-30 minutes, until the noodles are al dente and the soup has thickened.
Finish the Soup: Discard the bay leaves. Stir in 2-3 cups half-and-half, 1/2 cup heavy cream (if using), and thawed spinach, and warm through. Stir in 1 cup grated Parmesan cheese until melted and creamy. Adjust consistency with additional broth or half-and-half if desired, and season with salt and pepper to taste.
Serve: Ladle the White Chicken Lasagna Soup into bowls and garnish with shredded mozzarella, grated Parmesan, and a dollop of ricotta cheese. Serve hot and enjoy this cozy dinner idea!