In a small bowl, combine the minced garlic, chopped rosemary, chopped thyme, lemon juice and zest, olive oil, ground black pepper, and salt. Mix well to form a paste.
Rinse the leg of lamb and pat it dry with paper towels. Rub the marinade all over the lamb, ensuring it is well coated. Place the lamb in a roasting pan and cover with plastic wrap. Refrigerate for at least 4 hours, preferably overnight.
Preheat your oven to 375°F (190°C).
Place the quartered potatoes and carrot pieces around the lamb in the roasting pan. Drizzle with a little olive oil and season with salt and pepper.
Pour the white wine and chicken or lamb broth into the roasting pan. Cover the pan with aluminum foil and roast in the preheated oven for about 1.5 hours.
Remove the foil and continue to roast for another 30-45 minutes, or until the lamb is browned and cooked to your desired doneness. Baste the lamb and vegetables occasionally with the pan juices.
Once cooked, remove the lamb from the oven and let it rest for about 15 minutes before carving. This allows the juices to redistribute throughout the meat.
Carve the lamb into slices and arrange on a serving platter. Serve the roast lamb with the roasted potatoes and carrots, drizzled with the pan juices.
Enjoy your meal!