Preheat broiler. Place onion and garlic on a foil-lined baking sheet; toss with oil. Broil 5 minutes, 6 inches from heat, until onion is golden, stirring often.
Preheat oven to 425°. Transfer onion mixture to a square glass baking dish; top with chicken. Pour barbecue sauce over chicken; cover tightly with foil. Bake, in middle of oven, until chicken is cooked through (about 20 minutes).
Combine sour cream, vinegar, and honey; whisk well. Toss with coleslaw mix and pepper.
Shred chicken with a fork; top bottoms of rolls with chicken, onion, sauce mixture, and coleslaw. Place roll tops on sandwiches.
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