Freeze the steak for about 30 minutes. Remove from the freezer and slice into 1/8-inch thick slices, against the grain.
Place the beef in a large bowl. Pour in the bulgogi sauce. Toss to coat. Allow to marinate for 30-60 minutes.
Chop the lettuce. Place in a large serving bowl.
While the beef is marinating, make the pickling brine. Heat the water, vinegar, sugar, salt and pepper flakes in a sauce pot, until dissolved.
Using a vegetable peeler, peel the carrot. Discard the outer skin. Continue peeling to make ribbons. Place in a bowl. Add one-third of the brine.
Thinly slice the cucumber, place in another bowl with more brine.
Peel and core the green apple. Then, dice the apples into very small cubes. Place in a bowl with the remaining brine.
Prepare the dressing by whisking together the mayonnaise, vinegar, honey, soy sauce and sesame oil. Fold in the onions.
Heat the grill to high. Place a veggie pan on the grill. Working in batches, add the beef to the veggie basket. Grill for 3-5 minutes, until the beef is caramelized. Occasionally toss for even browning.
Drain the brine from the vegetables. Assemble the salad by adding the vegetables and cooked beef. Lastly, drizzle with dressing.