Remove meat from refrigerator 1 hour before grilling to reach room temperature. Heat grill on high for 10 minutes. Pat meat dry with paper towels and generously salt and pepper.
Place meat on hot grill without moving for 4 minutes. Turn meat over and cook for 3-4 more minutes; remove. Rest meat under tented foil 10 minutes.
Brush lettuce, avocados, and onion rings with olive oil. Season with salt and pepper. Reduce heat to medium-low and place vegetables on grill, oiled side down.
Brush opposite sides of lettuce and onions with oil and sprinkle with salt and pepper, to taste. Once veggies begin to char, turn lettuce and onions over and remove avocados. Continue cooking until the other side chars a little.
While warm, roughly chop lettuce, slice avocados, and separate onion rings.
Arrange lettuce, onions, avocados, tomatoes, and sliced steak on platter.
Drizzle dressing over top and sprinkle with bleu cheese.