Horseradish-Herb Rib Roast with Mushroom–Red Wine Sauce

Mix all of the measured ingredients in a small bowl until combined; set aside.

Cut (

24-inch-long pieces of kitchen twine; set aside.Rinse the roast under cold water to remove any bone fragments, pat it dry with paper towels, and place it on a cutting board. Following the line of the bones, cut the meat away from the bones in 1 piece. Rub the meat all over with the horseradish mixture. Fit the meat back onto the bones, matching the original position. Tie the meat onto the bones using one piece of twine in between each bone.

Remove the roast from the refrigerator and place it fat-side up in a roasting pan.

Let it sit at room temperature for 1 hour. Meanwhile, heat the oven to 450°F and arrange a rack in the lower third.Roast the beef for 45 minutes. Meanwhile, trim the stems from the mushrooms and cut them in half; set aside. Peel and cut the onion into eighths through the root end; set aside.

Remove the roasting pan from the oven. Scatter the mushrooms, onions, and rosemary around the roast, stir to coat them in the drippings, and spread them into an even layer.Reduce the oven temperature to 350°F and roast for 45 minutes. Stir the vegetables and continue to roast until an instant-read thermometer inserted into the center of the roast registers 125°F for medium rare, about 30 to 45 minutes more.

Transfer the roast to a cutting board, tent it loosely with aluminum foil, and let it rest for at least 20 to 30 minutes. Meanwhile, make the sauce.Using a slotted spoon, remove the vegetables and rosemary from the roasting pan to a medium bowl; set aside.

Pour the roast drippings into a small heatproof bowl and discard when cooled.

Place the roasting pan across 2 stovetop burners over medium heat. Return the vegetables and rosemary to the roasting pan, add the wine, and cook, scraping up the browned bits from the bottom of the pan, until the wine is reduced by about half, about 5 minutes.Increase the heat to medium high, add the beef broth, stir to combine, and bring to a simmer. Continue to simmer, stirring occasionally, until reduced by about half, about 5 minutes. Meanwhile, set a fine-mesh strainer in a large frying pan.

Pour the vegetable mixture through the strainer and discard the contents of the strainer.

Place the frying pan over medium-high heat and bring to a simmer. Reduce the heat to low and swirl in the butter 1 piece at a time, making sure each piece is completely melted before adding the next. Taste and season with salt and pepper as needed.

Remove the twine and bones from the roast, slice it, and serve with the sauce.