Spray 3 1/2- to 4-quart slow cooker with cooking spray. In cooker, place pork roast. In 1-cup measuring cup, stir together barbecue sauce, honey, balsamic vinegar, soy sauce, ginger and pepper; pour over pork.
Cover; cook on Low heat setting 6 to 7 hours.
Place carrots around pork. Increase heat setting to High. Cover; cook about 30 minutes longer or until carrots are crisp-tender. Remove pork from cooker to cutting board with slotted spoon. Cut pork into slices; place on serving platter. Top pork with sauce and carrots.