Place cabbage leaves in the bottom of the slow cooker. Place pork on top of cabbage (fat cap side up) and add ketchup, peppers, and adobo sauce. Pour Cheerwine on top and cook on high for 4-5 hours (or on low for 8 hours). Halfway through the cooking time, flip pork over.
At the end of the cooking time, remove tender meat and cabbage from the slow cooker and place on large cutting board or platter. Discard cabbage leaves (or eat them as a snack) and shred pork using two forks, pulling the meat and the forks away from each other. Place shredded pork back into the slow cooker and continue to cook on low for an additional hour. Top onto a roll or bun of choice and serve.