In small nonstick skillet, heat oil over medium-low heat. Add onions. Cook and stir 3 to 4 minutes or until tender, but not browned. Add garlic. Continue cooking and stirring 2 to 3 minutes. Season with salt and pepper; cool completely.
Meanwhile with sharp knife, cut a pocket in side of each beef steak. Start 1/2 inch from one long side of steak and cut horizontally through center of steak to within 1/2 inch of each side. Spread half of garlic mixture inside each steak pocket. Secure openings with wooden toothpicks.
Place steaks on grid over medium, ash-covered coals. Grill, covered, 22 to 24 minutes for medium rare to medium doneness; turn occasionally. Remove wooden toothpicks. Carve steaks crosswise into 1/2-inch thick slices.