Position racks in the top and bottom of the oven; place a rimmed baking sheet on the bottom rack. Preheat the oven to 450 degrees F. Toss the potatoes with 2 tablespoons olive oil, 1/2 teaspoon salt and a few grinds of pepper in a bowl. Spread on the hot pan and bake, turning once, until golden and tender, 18 to 20 minutes.
Meanwhile, whisk the steak sauce, vinegar, mustard and remaining 2 tablespoons olive oil in a large bowl; set aside. Heat a large ovenproof skillet over high heat. Brush the steak on both sides with olive oil and season with salt and pepper. Add to the skillet and cook until browned, about 2 minutes per side. Brush the top of the steak with about 1 tablespoon of the vinaigrette. Transfer the skillet to the top oven rack and cook until a thermometer inserted sideways into the steak registers 120 degrees F for medium rare, about 4 minutes. Transfer to a cutting board and let rest 5 minutes, then thinly slice against the grain.
Whisk 2 tablespoons of the juices from the skillet into the bowl with the vinaigrette. Add the romaine, tomato and chives; season with salt and pepper and toss. Divide the salad among plates and top with the potatoes, steak, blue cheese and more chives.