Remove the steak from the refrigerator 30 minutes before cooking. Heat a large heavy-bottomed skillet over medium-high heat. Pat the steak dry and season generously with salt and pepper on all sides. Place the steak, standing up on the strip of fat, in the pan and hold it with tongs until the fat renders and the pan is slick, about 2 minutes.
Place the steak flat in the pan and sear until deep brown on one side, 4 to 5 minutes. Turn and cook on the other side until a thermometer inserted sideways into the thickest part registers 120 degrees for medium-rare, 3 to 4 more minutes. Transfer to a cutting board and let rest 10 minutes. Reserve the drippings in the skillet.
Add the shallot to the drippings and cook over medium heat until golden, about 2 minutes. Add the wine and scrape up any browned bits with a wooden spoon. Bring to a boil and cook until reduced by half and slightly syrupy, about 7 minutes; remove from the heat. Whisk in the butter, one piece at a time, to make a glossy sauce. Add 1/2 teaspoon salt and 1/4 teaspoon pepper or season to taste. Slice the steak against the grain and serve with the sauce.