Heat a chargrill pan or barbecue grill over high heat. Brush steak with 2 tsp oil and season. Drizzle 1 tbs oil over mushrooms and season. Grill beef for 4 minutes on each side for medium, and mushrooms for 3 minutes on each side. Transfer steak and mushrooms to a plate to rest, loosely covered with foil, for 5 minutes.
Meanwhile, to make the miso dressing, whisk all the ingredients together in a small bowl with a fork to combine.
Toss asparagus in remaining oil and grill in the same pan for 1-2 minutes, turning, or until tender and crisp, and light grill marks appear.
Place sesame seeds on a small plate. Thickly slice mushrooms and press one side into seeds to coat. Thinly slice beef.
On a large serving platter, combine lettuce, edamame, asparagus and beef. Top with mushrooms and drizzle over dressing to serve.
