Place chicken in a 3-4 quart slow cooker with chicken broth, cover and cook on LOW for 4-6 hours.
Remove chicken from cooker using a slotted spoon and drain the broth from the slow cooker. Place chicken on a cutting board and pull chicken into shreds, discarding any fat.
Place chicken back in the cooker and pour Caesar dressing, Parmesan cheese, parsley, and pepper over the top. Stir until mixed evenly. Cover and cook on HIGH heat for 30 minutes or until mixture is hot.
Spoon 1/4 cup mixture onto each toasted slider bun if you are making sliders or more for regular sized buns. Sprinkle with extra Parmesan cheese if desired and shredded lettuce to serve.