Remove steak from refrigerator 10 minutes before cooking; slice mushrooms and mince garlic, tear lettuce leaves into serving-size pieces.
Heat a large skillet over high until very hot; season steak with salt and pepper, sear 3–4 minutes per side for medium-rare, reaching 145°F internal temperature, then transfer to a cutting board to rest 3 minutes.
In same skillet, melt 2 tablespoons butter over medium-high, add mushrooms and garlic, cook 5 minutes until golden, stirring often, then stir in remaining 1 tablespoon butter.
Slice rested steak into 0.5-inch strips; arrange lettuce leaves on plates, fill with steak and mushroom mixture, top with blue cheese.