Set grill to medium-high. Season chicken with salt and pepper. Grill chicken 4 minutes per side. To a small bowl, add 3 tablespoons barbecue sauce and brush chicken with some of the sauce. Continue grilling 1 to 2 minutes, until cooked through, turning occasionally and brushing with more sauce. Grill the buns, cut-sides down, 1 minute, until toasted.
Meanwhile, in a large bowl, whisk together mayonnaise, vinegar, and mustard. Add Brussels sprouts and carrots and toss to combine. Season with salt and pepper.
Remove chicken from grill. Chop chicken and toss with remaining 4 tablespoons barbecue sauce. Divide chicken among bottom buns and top each with slaw and tops of buns.
Hannaford fresh Magazine, September 2023