In large skillet, heat 1 tbsp (15 mL) olive oil over medium-high heat. Stir in spinach, garlic, thyme, ½ tsp (2 mL) salt and ¼ tsp (1 mL) pepper. Cook 3 to 4 min. or until spinach is wilted. Cool completely. Use the back of a wooden spoon to press out excess liquid.
Place flank steak on a cutting board. With the grain of the steak running horizontally, use a long sharp knife to slice into the mid-point of the cut. Slice into the meat along the grain of the steak, opening it up like a book, being careful to leave it in one piece (do not cut through the other side.) Cover top and bottom with plastic wrap and pound with a meat tenderizer or flat side of a small, heavy saucepan to ¼-in. (5-mm) thickness.
Place sliced cheese, red pepper pieces and spinach mixture in an even layer on cut side of steak, leaving a 1-in. (2.5-cm) border. Tightly roll the steak into a log -- with the grain running along its length -- tucking in the edges as you roll to enclose the filling. Secure log with butcher’s twine. Coat with remaining olive oil. Season with remaining salt and pepper.
Grill on barbecue preheated to medium-high, turning occasionally, for 8 to 10 min., or until browned. Turn off the burner directly under the steak, but keep the other burner(s) on. Grill an additional 15 to 20 min. or until an internal meat temperature of 140° F (60°C) is reached for medium-rare, or until cooked to desired doneness. Transfer the steak to cutting board, cover loosely with foil, and let rest 10 min. Remove and discard butcher’s twine. Cut steak crosswise, into ½-in. (1-cm) thick slices.