Melt butter in a 5-quart pot over medium heat; cook and stir onion and garlic in melted butter until onion is translucent, about 5 minutes. Stir chicken broth and Alfredo sauce into onion mixture; cook until heated through, about 5 minutes. Stir in sour cream and cooked chicken; simmer for 15 minutes.
Mix cheese tortellini and spinach into chicken mixture, cover pot, and simmer for 20 minutes. Season with salt and pepper.
Divide soup into bowls and sprinkle with Parmesan cheese.