Place steak in large resealable food storage bag. Pour 1/4 cup of the soy sauce over steak; seal bag. Refrigerate 20 minutes, turning bag halfway through marinating time.
Position broiler rack 3 to 4 inches from heat. Spray broiler pan with cooking spray. Stir together remaining soy sauce, honey, vinegar and bamboo shoots in medium bowl. Stir together cornstarch and water; blend into soy sauce mixture and set aside.
Place steak on broiler pan; discard bag with marinade. Broil 16 to 20 minutes for medium-rare to medium doneness, turning once. Let stand 10 minutes before slicing.
Meanwhile, heat medium skillet over high heat; toast sesame seeds until lightly browned. Add soy sauce mixture; cook and stir 2 minutes or until thickened and bubbly. Remove from heat. Cut steak across the grain into thin pieces. Toss with prepared sauce. Serve with rice, if desired.