01 - Preheat the oven to 300°F.
02 - Pat the leg of lamb dry with paper towels. Use a sharp knife to make deep slits all over the lamb, inserting sliced garlic and chopped rosemary into each slit.
03 - Rub the entire surface of the lamb with olive oil, kosher salt, black pepper, remaining rosemary, and thyme leaves.
04 - Place the sliced onions, carrot chunks, and celery pieces in the bottom of a large roasting pan, then place the lamb on top of the vegetables.
05 - Pour the white wine or chicken broth around the lamb in the pan, avoiding pouring directly over the meat.
06 - Cover the roasting pan tightly with aluminum foil and roast the lamb for 3 hours at 300°F.
07 - Remove the foil, increase the oven temperature to 400°F, and roast the lamb uncovered for an additional 30 minutes to develop a browned crust.
08 - Transfer the lamb to a cutting board, cover loosely with foil, and allow it to rest for 20 minutes before carving.
09 - Strain the pan juices, skim off any excess fat, and serve the sauce alongside the carved lamb.