1Prepare barbecue (medium-high heat). Whisk oil and butter in small bowl. Whisk mustard and next 3 ingredients in another small bowl.
2Run 2 thin metal skewers or soaked bamboo skewers parallel through each onion slice, placing skewers about 1 1/2 inches apart to keep slice intact. Trim ends of bamboo skewers. Brush both sides of onion slices with oil mixture. Place onions on grill and cook until beginning to char, turning and brushing often with oil mixture, about 11 minutes. Brush top side of onions with mustard mixture and cook until mixture begins to bubble, about 2 minutes. Turn onions; brush with mustard mixture and grill until beginning to caramelize, about 1 minute longer. Transfer onions to plate. Brush with mustard mixture.