Thinly slice steak. Add to marinade (green onions, soy sauce, sherry, ginger, garlic, sugar and sesame oil) and set aside for 10-15 minutes.
Meanwhile, put cucumber, mango and mint on small plates and place on dining table. Line a baking tray with foil; spread beef and marinade on it. Broil about 4 inches from heat, flipping once, until beef is cooked and has crispy edges, 5 to 8 minutes. Transfer to a serving plate.
Divide lettuce leaves equally among 4 plates and have diners assemble their rolls with beef, cucumber, mango and mint, then roll snugly. (Rice can be added to the rolls, if desired.)
Per serving: 287 calories, 30 g protein, 10 g fat (4 g saturated fat), 16 g carbohydrates, 2 g fibre, 84 mg cholesterol, 283 mg sodium.