Step 1

Preheat oven to 450°F with rack 6 inches from heat. Arrange chicken, skin side up, on a rimmed baking sheet lined with aluminum foil. Season with ¼ teaspoon each salt and black pepper. Roast until skin is crisp, about 25 minutes.

Step 2

Meanwhile, combine coleslaw, mini peppers, sour cream, mustard, vinegar, honey, and remaining ¾ teaspoon salt and ¼ teaspoon black pepper in a large bowl; refrigerate.

Step 3

Remove chicken from oven. Increase temperature to broil. Turn over chicken and brush with 2 tablespoons barbecue sauce. Broil until sauce is bubbling, 2 to 3 minutes. Turn chicken skin side up. Brush with ¼ cup barbecue sauce. Broil until sauce is bubbling, 2 to 3 minutes. Brush tops with remaining ¼ cup barbecue sauce. Broil until an instant-read thermometer inserted in thickest portion of chicken reads 165°F, 3 to 5 minutes. Serve with coleslaw.