Grill beef steak, covered, 11 to 15 minutes (for a preheated gas grill, 13 to 16 minutes), turning occasionally.
While the steak is grilling, combine all of the dressing ingredients in a bowl until smooth. Arrange lettuce, mango, avocado carrot, and bell pepper on a serving platter.
Carve steak into slices and season with salt. Arrange beef over salad.
Drizzle with dressing and sprinkle with peanuts. Serve immediately; squeeze lime wedges over salad, as desired.