1Heat coals or gas grill for direct heat. Make horizontal cut in side of each steak, forming a pocket (do not cut through to opposite side).
2Mix pesto and cheese; spread evenly on insides of pockets; press pockets closed. Drizzle oil over beef.
3Cover and grill beef 4 to 5 inches from medium heat 12 to 14 minutes for medium doneness, turning once. To serve, cut beef into thick strips.