Allow the filets mignons to stand at room temperature for 10 to 20 minutes before grilling. Lightly brush or spray both sides with oil. Season evenly with the salt and pepper. Grill over Direct High heat until cooked to your desired doneness, 8 to 10 minutes for medium-rare, turning once. Transfer each filet to a serving plate and place a tablespoon of the butter on top to melt. Serve warm.