Sprinkle chicken with ½ teaspoon each of the salt and pepper.
In 12-inch skillet or Dutch oven, heat oil over medium-high heat.
Add chicken; cook 2 minutes on each side or until browned.
Transfer chicken to large shallow roasting pan.
In small bowl, mix syrup, broth, orange peel, orange juice, bourbon, mustard, and remaining ½ teaspoon each salt and pepper.
Place Brussels sprouts and carrots around chicken in pan; dot with butter.
Drizzle vegetables with ¼ cup of the orange mixture.
Brush chicken with ¼ cup orange mixture.
Roast uncovered 1 hour 15 minutes, brushing every 20 minutes with orange mixture and stirring vegetables once, or until meat thermometer reads at least 165°F.
In 1-quart saucepan, heat remaining orange mixture to boiling.