Heat the oven to 375 F. Lay the lamb out flat, cut-side up, on a clean surface. Sprinkle the meat with kosher salt and pepper, then arrange half of the thyme, rosemary, and sage and all of the garlic on the meat. Roll the meat around the herbs and tie with twine at 1 ½-inch intervals.

Heat the oil in an ovenproof skillet or roasting pan over medium heat until it slides easily across the pan. Salt and pepper the outside of the lamb, then brown it on all sides, about 25 minutes. Transfer the skillet to the oven.

Cook the lamb for about 45 minutes. Add the butter and remaining herb sprigs and continue cooking the lamb, basting occasionally, for about 15 minutes. (The lamb is medium rare when a thermometer inserted in the center indicates an internal temperature of 125 F.) Remove the lamb from the oven, cover loosely with foil, and allow the meat to rest for about 10 minutes. Slice and serve sprinkled with coarse sea salt.