Combine chicken, tomatoes, broth, onion, bell pepper, garlic, Italian seasoning, pepper, salt, crushed red pepper, and bay leaf in a 4-quart slow cooker. Cover and cook on High until the chicken is tender and an instant-read thermometer inserted into the thickest part of the chicken registers 165 degrees F, about 3 hours. Remove and discard the bay leaf. Transfer the chicken to a plate; let rest for 10 minutes.

Stir pasta into the mixture in the slow cooker; cover and cook on High until the pasta is tender, about 30 minutes.

Coarsely shred the chicken and stir it back into the soup, along with basil and parsley. Ladle the soup evenly into 6 bowls; sprinkle with Parmesan and garnish with parsley, if desired.