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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This recipe needs to be adjusted before it tastes like a proper pulled chicken sandwich:
First, only half of the onions are needed for each pound of chicken, or it will be too oniony.
The chicken needs to be salted and peppered before pouring the barbecue sauce, or it will be very bland and since chicken thighs produce a lot of "gravy" when cooked and will water down the sauce.
It also took double the cooking time for the chicken to be cooked through.
I had to transfer the chicken to a bowl before shredding because there was so much watery gravy in the baking dish, and added some of the cooked onions drained with a slotted spoon. A few tablespoons of extra barbecue sauce had to be added to make it sufficiently tasty.
Next time I cook the chicken I'd probably use a mix of boneless chicken thighs and breasts, since the latter doesn't produce as much moisture. I didn't try the coleslaw part but if I do, I probably wouldn't use sour cream: I'd sub lowfat mayo or plain Greek yogurt.
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