FOR South Carolina BBQ Mustard Sauce: Melt butter in saute pan on medium-high heat. Add onions; cook until tender. Transfer to food processor. Add remaining ingredients; process until well blended.
FOR Turkey Drumsticks: Coat drumsticks with oil. Grill on high heat 5 min., turning frequently, until browned on all sides. Place on sheet pan.
BAKE in 450ºF standard oven 15 min. or until almost done. Remove from oven. Brush each drumstick with 2 Tbsp. prepared sauce. Bake 5 min. or until internal temperature reaches 165ºF. Let stand 15 min., loosely covered, before serving.