Place one of the chicken pieces in between two plastic sheets or in a large plastic bag. Flatten to an even thickness, about 3/4-inch. Repeat with remaining pieces.Alternatively, for pieces about 2-inches thick or larger, cut in half horizontally to create two cutlets, repeat with the remaining pieces.
In a small bowl, combine brown sugar, cumin, paprika, salt, chili powder, garlic powder, onion powder, and black pepper.
Evenly sprinkle the dry rub over each piece of chicken, about 1 teaspoon per side.
Cook on the Stovetop: Heat a grill pan over medium-high heat. Evenly grease the surface with about 1 tablespoon olive oil. Once the oil is hot, working in batches, add the seasoned chicken. Cook until char marks appear, about 4 to 6 minutes. Flip and cook about 3 to 5 minutes. Clean and grease the pan as needed, repeat with the remaining pieces.Cook on the Barbecue: Heat grill over medium-high heat. Clean and oil the grill grates. Once hot, add the seasoned chicken. Cover with the lid and cook until char marks appear, about 3 to 4 minutes. Flip the pieces and cover, about 3 to 4 minutes.
Cook until the internal temperature reaches between 160 to 165ºF (71 to 74ºC). Clean and grease the grates as needed. Rest the cooked chicken for 5 minutes.
Coleslaw
In a medium bowl, combine yogurt, mayonnaise, apple cider vinegar, honey, paprika, salt, and pepper.
In a large bowl, combine green cabbage, red cabbage, and carrots. Add the dressing and toss to combine. Season with salt and pepper to taste. If not used immediately, cover and refrigerate.
To Serve
Use two forks to shred into smaller pieces. Combine shredded chicken with barbecue sauce.
Right before serving, grill the buns cut-side down. Heat until toasted, about 2 to 3 minutes.
Add pulled chicken to each toasted bottom bun and top with coleslaw.
Notes
Using leftover chicken: Shred leftover chicken pieces or rotisserie chicken into smaller pieces. You will need about 5 cups. Heat in the microwave on high power until hot. Toss with some dry rub and barbecue sauce.
Storing: Cover and refrigerate grilled chicken up to 5 days in advance. Wait to toss with the barbecue sauce until ready to serve. Store the coleslaw in an airtight container for up to 1 day in the refrigerator.