Poach the chicken. Bring the chicken broth and cheese rind, if using, to a boil in a Dutch oven or soup pot over high heat. Add the chicken breasts, cover, and immediately turn the burner off. Let the pot stand for 20 minutes, or until the chicken is no longer pink in the center and an instant read thermometer reads 165ºF. Transfer the meat to a cutting board and chop it into bite-size pieces and set aside. Discard the cheese rind.

Add the vegetables. Add the carrots, celery, and Italian seasoning to the pot and bring to a simmer over medium-high heat. Simmer until vegetables are just tender, 8 to 10 minutes.

Add the tortellini. Add the tortellini to the pot, reduce heat to maintain a gentle simmer, and cook until the pasta is tender, 3 to 4 minutes.

Stir in the chicken and greens. Reduce heat to low and stir the chicken and the baby greens. Cook, stirring occasionally, until the greens are just wilted, 2 to 3 minutes.

Finish and serve. Season the soup with salt and pepper. Divide the soup among deep bowls and sprinkle the parmesan cheese over the top and serve immediately.