In a large pot or Dutch oven over medium heat, melt the butter. Whisk in the flour and cook for 1-2 minutes to create a roux. Add the diced carrots, onions, and minced garlic, along with the Italian seasoning, chili flakes (if using), and nutmeg. Stir well and cook until the vegetables soften, about 3-4 minutes.
Pour in the chicken broth and bring to a simmer. Season with salt and pepper. Add the chopped air-fried chicken thighs to the pot. Cover and let it simmer for about 15 minutes.
Bring the soup to a gentle boil and stir in the broken lasagna noodles. Cook until the noodles are al dente, approximately 10 minutes. If you prefer softer noodles, cook for an additional 2-3 minutes.
Add the chopped spinach to the pot and stir until wilted, which should take about 2 minutes.
Reduce the heat to low. Stir in the half 'n' half, followed by the shredded mozzarella, grated Parmesan, and softened cream cheese. Continue stirring until the cheeses are melted and the soup is creamy and well combined. Adjust seasoning if needed. Add some chicken broth or water if you want a thinner consistency.
Let the soup cool slightly, for about 5-10 minutes, to allow it to thicken up a bit. Ladle the soup into bowls and serve warm with a sprinkle of Parmesan cheese on top.