Heat the broiler to high and set a rack directly under it. Season the steaks with 1 tsp. salt and a few grinds of pepper.
Melt 2 Tbs. of the butter. Cut the potato crosswise into thin, uniform slices about 1/8 inch thick. Spray a heavy-duty rimmed baking sheet with cooking spray. In a large bowl, gently toss the potato slices with the melted butter, chopped rosemary, 1/2 tsp. salt, and a few generous grinds of pepper. Arrange the potato slices in a single layer on the baking sheet and broil until they begin to brown, 2 to 4 minutes. Flip and broil until the second sides are lightly golden brown and the potatoes are slightly crisp around the edges, 3 to 5 minutes. Set aside and keep warm.
Set a heavy skillet over high heat for 1-1/2 minutes. Carefully set the steaks in the pan and sear without moving for 2 to 3 minutes. Flip the steaks and cook for another 2 to 3 minutes for medium rare. Remove the pan from the heat and add the remaining 2 Tbs. butter and the rosemary sprigs to the pan. Let the steaks rest in the pan for 5 minutes, basting them occasionally with the pan juices. Carve the steaks into 1/4-inch slices and sprinkle with salt.
Arrange the steak and potatoes on two dinner plates and drizzle the steak with the rosemary-butter pan sauce. Serve immediately.
nutrition information (per serving):
Photo: Scott Phillips