Add the first five ingredients in the bowl of a slow cooker and toss to combine. Season with salt and pepper. Cook on high heat for 3-4 hours.
When the chicken is cooked, drain most of the liquid. Shred the breast meat with two forks in the bowl of the slow cooker. Toss with more caesar dressing.
Toast and butter ciabatta rolls, if desired. Top bottom halves with romaine, shredded chicken and shaved Parmesan. Place top halves on top and serve warm.