Combine the first 12 ingredients — ketchup through pepper — to a 6 quart crock pot then whisk to combine. Add chicken halves then cover completely in sauce and cook on low for 4 hours or until chicken shreds easily with two forks.
Remove 2 cups cooking liquid then pour into a saucepan over medium-high heat and bring to a simmer. Reduce heat to medium then continue to simmer until the sauce has reduced to a sauce consistency — sauce will continue to thicken as it cools. Meanwhile, shred chicken with 2 forks then return to crock pot with remaining liquid and stir to combine.
For the Crunchy Apple Slaw:
In a large bowl whisk together olive oil, apple cider vinegar, honey, lime juice, salt and pepper. Add cabbage and apples then toss to combine.
Place shredded chicken on buns then top with reduced sauce and slices of smoked gouda. Broiler until the cheese has melted then top with Crunchy Apple Slaw and serve.