Poach the chicken by bringing 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 the pot, then immediately turn off the heat. Let the pot sit for 20 minutes, or until the chicken is cooked through and an instant-read thermometer registers 165ºF. Remove the chicken to a cutting board, chop it into bite-sized pieces, and set aside. Discard the cheese rind.
Add the carrots, celery, and Italian seasoning to the pot, then bring the mixture to a simmer over medium-high heat. Cook until the vegetables are just tender, about 8 to 10 minutes.
Stir in the tortellini, lower the heat to maintain a gentle simmer, and cook until the pasta is tender, about 3 to 4 minutes.
Reduce the heat to low, then add the chopped chicken and baby greens. Cook, stirring occasionally, until the greens have just wilted, about 2 to 3 minutes.
Season the soup with salt and freshly ground black pepper to taste. Ladle the soup into deep bowls, sprinkle with the grated Parmigiano Reggiano, and serve immediately.