Pour the chicken broth into the bowl of your slow cooker, and then add the chicken breasts. Cover, and cook on low for 4-6 hours, or until the chicken's cooked through.
Remove the lid and transfer the cooked chicken to a cutting board. Shred using two forks or a pair of meat claws. Empty any liquid from the bowl of the slow cooker, place it back in the insert, and transfer the chicken back to the bowl.
Add the dressing, 1/2 the cheese, parsley, pepper flakes, and salt & pepper to taste. You'll want to use twice as much freshly ground black pepper as salt. Stir everything to evenly combine. Cover, and cook another 30-45 minutes on high, stirring at least once.
Top the bottoms of each bun with several leaves of lettuce. Add an equal amount of the hot Caesar chicken to each bun, spreading a bit to cover until all the buns are prepped. Sprinkle the remaining cheese evenly out over all the buns. Top all the sandwiches with top buns. Serve immediately.
Like any sandwich, you can really serve these with whatever you want. We tend to serve them with a handful of potato chips and fresh fruit salad.