Season the chicken with the salt and black pepper and put it in a 6-quart slow cooker.
Add the onion, garlic and broth, cover and cook on low until the breasts reach 165°F, 3 1/2 to 4 hours.
Move the chicken to a board, cut it into bite-size pieces and return it to the cooker.
Switch to high, add the tortellini and cover until almost tender, 15 to 20 minutes.
Fold in the cherry tomatoes and cook for 5 minutes more.
Turn off the cooker, stir in the pesto and Parmesan and serve as soon as the sauce coats the pasta.