Place tenderloins, olive oil, salt, pepper, garlic, vinegar, mustard and onion in a zipper-lock bag. Shake bag to combine ingredients. Refrigerate for 1 to 4 hours.
Remove bag from refrigerator, and leave at room temperature for 15 to 20 minutes. Remove meat and onion from bag. Discard marinade. Place meat and onion in a preheated heavy-duty, oven-safe skillet (like cast iron), and place immediately under a preheated broiler, about 5 to 6 inches from the heat source. Broil for 4 to 5 minutes, then remove skillet from broiler. Transfer meat to a plate or cutting board, and let rest for a few minutes. Meanwhile, whisk butter into skillet.
To serve, slice tenderloin, and arrange on plates or platter with onion. Drizzle butter sauce over.