To prepare chicken, combine the water, sugar, salt, peppercorns, thyme, parsley, and bay leaf in a saucepan. Bring to a simmer and cook until the sugar and salt dissolve. Remove from the heat and let the mixture cool for 30 minutes. Stir in the ice and pour the mixture into a large baking dish or bowl. Add the chicken thighs, cover and chill for 4 hours or up to overnight. Drain and discard the brine.
Preheat an indoor smoker to 200°F. Place the chicken thighs in the smoker and smoke for 3-4 hours.
Alternately, preheat the oven to 225°F and roast the chicken thighs for 3-4 hours or until internal temperature reaches 165°F.
Transfer the chicken to a bowl along with any juices, and shred the chicken.
Make the potato salad: In a medium pot with a steamer basket, add 1 inch of water and the potatoes. Bring to a simmer, cover, and cook for 8 to 10 minutes, or until fork-tender. Drain the potatoes.
In a large bowl, combine the remaining potato salad ingredients. Fold in the potatoes and season with salt and pepper to taste.
To make the coleslaw, combine the mustard, mayonnaise, vinegar, sugar, salt and pepper in a large bowl. Fold in the cabbage, onion and carrots.
To make the BBQ sauce, in a medium bowl, whisk together the ketchup, honey, vinegar, chile paste, tamari, Worcestershire, cumin, onion powder, garlic powder, chile powder, and both paprikas.
Toss the shredded chicken with the BBQ sauce to coat.
Serve the chicken on hamburger buns alongside coleslaw and potato salad.