Heat oven to 425° F. Combine the butter and blue cheese in a small bowl; set aside.
Place the potatoes in 1 inch of water in a microwave-safe dish, cover, and microwave on high until tender, 7 to 10 minutes. Drain and rinse with cold water to stop the cooking; halve.
Heat 1 tablespoon of the oil in a large ovenproof skillet on high heat. Season the steak with 1 teaspoon each salt and pepper. Cook until browned, 3 to 4 minutes per side. Add the potatoes to the skillet with the steak. Transfer to oven and cook until an instant-read thermometer inserted in the thickest part of the steak registers 130° F for medium-rare, 7 to 10 minutes. Transfer the steak to a cutting board and top with half the blue cheese butter; let rest for 10 minutes before slicing against the grain.
Toss the lettuce, tomatoes, vinegar, the remaining 2 tablespoons of oil, and ¼ teaspoon each salt and pepper in a large bowl.
Serve the steak and potatoes with the remaining blue cheese butter alongside the salad.
