1If pesto is not refrigerated, freeze 15 minutes to firm. Heat gas or charcoal grill.
2Make a horizontal cut into side of each steak, cutting to but not through opposite side and leaving about 1/2 inch uncut at each side, to form a pocket. Spoon firm pesto evenly into pockets. Secure openings with toothpicks. Sprinkle pepper over both sides of beef.
3Place beef on grill. Cover grill; cook over medium heat 5 to 10 minutes on each side for medium doneness (160°F) or until desired doneness. Broiling Directions: Set oven control to broil. Place stuffed beef on rack in broiler pan. Broil with tops 4 to 6 inches from heat 9 minutes; turn. Broil 5 to 10 minutes longer for medium doneness or until desired doneness.