Preheat the oven to 375 degrees . Season both sides of the steak with salt and pepper. Heat the olive oil in a medium skillet over medium-high heat. When the olive oil is hot, add the steak and cook until well seared, about 4 to 5 minutes per side for medium-rare. Transfer the steak to a plate.
Meanwhile, place the chopped onion, carrot and celery in the skillet, lower the heat to medium and saute the vegetables until browned, about 4 minutes. Add the wine and scrape any browned bits off the bottom of the pan. Add the rosemary and simmer until the liquid is reduced by two-thirds. Turn off the heat, strain the sauce into a bowl, discarding the solids, and return the sauce to the skillet.
Cut the butter into small pats and gently swirl them into the sauce, then season with salt and pepper. Transfer the steak to a cutting board and slice it across the grain into 1/4-inch-thick slices. Serve the steak with the Brunello sauce.