How to Make It
Preheat the oven to 325°. Using a sharp paring knife, make 1-inch-deep slits all over the surface of the meat. Rub salt and pepper all over the outside and in the slits of the roast. Heat the olive oil in a very large skillet. Add the roast, meaty side down, and cook over high heat until browned, about 10 minutes. Add the butter, garlic and thyme and cook over moderate heat, basting the roast with the butter, for 5 minutes.
Transfer the roast to a medium roasting pan, bone side down. Press the cut side of the garlic halves and the thyme sprigs onto the surface of the meat and roast, turning the pan occasionally, for about 3 1/2 hours; the meat is done when an instant-read thermometer inserted in the center registers 125°. Let rest for 15 minutes.
Combine all of the ingredients in a bowl.
Carve the roast off the bone, then thinly slice. Serve with the horseradish sauce.
Piment d'Espelette, a Basque red chile powder, is available at specialty food stores and online at vannsspices.com.