Grilled Pesto-stuffed Steaks

2 Beef rib eye steaks, 1 1/2 " thick (about 2 pounds)
1/4 c Pesto
2 tb Finely shredded Parmesan cheese
1 tb Olive or vegetable oil
1/3 c Finely shredded Parmesan cheese
 
Heat coals or gas grill. Make a horizontal cut in side of each beef steak, forming a pocket (do not cut through to opposite side).

Mix pesto and 2 tablespoons cheese; spread evenly on insides of pockets; press pockets closed.

Drizzle oil over beef. Roll beef in 1/3 cup cheese until well coated.

Cover and grill beef 4 to 5 inches from medium heat 12 to 14 minutes for medium doneness, turning once. To serve, cut each beef steak into thick strips.

Makes 4 servings.