Trim fat from steak. Rinse meat, pat dry, and rub with 1 tbsp. soy sauce and the oil.
Lay steak on an oiled cooking grate over a solid bed of very hot coals or highest gas heat (you can hold your hand 1 to 2 in. above grate for only 1 to 2 seconds); cover gas grill. Cook until firm when pressed on thin end but still quite pink inside (cut to check), 8 to 10 minutes; turn over halfway through. Transfer steak to a plate. Let cool at least 30 minutes.
On a board with a sharp knife, cut steak across the grain, straight up and down, into very thin slices, keeping slices in place. Cut steak lengthwise to divide the slices into halves or quarters.
Combine 4 tbsp. soy sauce, broth, black beans, sherry, ginger, vinegar, cornstarch mixture, and brown sugar. In a large frying pan, stir dressing over high heat until boiling. Add steak and juices; stir until hot, about 2 minutes. Remove from heat.
Put peanuts in a resealable plastic bag and coarsely crush with a meat mallet or bottom of a small, heavy skillet. Stack lettuce leaves and cut thinly widthwise.
Mound lettuce equally into 6 wide salad or soup bowls. Spoon hot steak and dressing onto greens; sprinkle with bell pepper, green onions, and peanuts. Garnish with cilantro and serve immediately.
Note: Nutritional analysis is per serving.