Warm 2 tablespoons of the olive oil in a deep 12-inch skillet over medium heat. Add the chicken and cook, stirring often, until the pieces are fully cooked, about 3 to 4 minutes. Season with Italian seasoning, salt, and pepper. Transfer the cooked chicken to a plate and keep warm.

Add the remaining tablespoon of olive oil to the skillet. Stir in the onion and cook for 2 to 3 minutes, or until softened. Add the garlic and cook for about 1 minute.

Pour in the broth, tomatoes, pasta, crushed red pepper, and a pinch of salt and pepper. Return the chicken to the skillet and stir well. Bring the mixture to a boil, then cover, reduce the heat to medium-low, and let it simmer until the pasta is tender, about 15 minutes.

Stir in the half-and-half and mozzarella, letting the sauce heat gently until the cheese melts.

Remove the skillet from the heat and fold in the spinach until it wilts. Sprinkle with Parmesan before serving.