Heat the oven to 450°F and line an 18-by-13-inch rimmed metal sheet pan with foil. Toss potatoes with 1 tablespoon oil, rosemary and 1/4 teaspoon salt and roast for 20 minutes.
Pat steak dry and rub with Worcestershire, garlic powder, pepper, 1 teaspoon oil and 1/4 teaspoon salt. Toss green beans with remaining oil and salt.
Turn potatoes, add green beans and roast for 7 minutes more. Move the vegetables toward the edges and lay steak flat in the center.
Switch to broil and place the pan about 6 inches from the element. Broil steak for 4 to 6 minutes per side, watching the vegetables and turning any dark pieces inward, until the steak reaches 145°F.
Transfer steak to a clean board and rest for at least 3 minutes, preferably 5. Slice thinly across the grain and serve with the potatoes and green beans.