Preheat the BBQ grill.
To butterfly the steak, place steak on a cutting board with 1 long side facing you. Trim short edges as needed to form a rough rectangle. Press 1 hand flat on steak to steady it. Holding knife parallel to cutting board and starting on one short side, slice horizontally to within 3/4 inch of the opposite side. Open cut steak like a book.
Sprinkle cut sides of steak evenly with salt & pepper and garlic, Top with basil, leaving a 1“ border on all sides. Arrange bell peppers and cherry bell peppers evenly over basil. Overlap cheese slices on top of peppers. Roll up steak away from you into a tight cylinder.
Tie cylinder crosswise at about 1½” intervals starting from center and working out toward the ends using kitchen twine. Cover outside with oil / non-stick spray. Season outside with salt and pepper or dry steak seasoning of choice.
Grill steak on BBQ on low/medium heat, turning occasionally Cook until internal temperature of steak is 130° - 135°F (medium-rare), ~30 mins.
Transfer to a cutting board. Let rest 10 mins. Remove and discard kitchen twine. Cut crosswise into slices.