Preheat the oven to 400 degrees F (200 degrees C). Bring a large pot of water to a boil. Add the potatoes and carrots; boil for about 3 minutes. Drain and set aside.
Rinse the leg of lamb and pat dry. Place it in a roasting pan and season generously with salt and pepper. Rub the salt and pepper into the meat. Use a small knife to make incisions big enough for a garlic clove to fit in all over the leg. Stuff the garlic cloves into the holes. Spoon the mustard over the lamb and rub it in as well.
Roast, uncovered, in the preheated oven for about 30 minutes. Reduce the oven temperature to 375 degrees F (190 degrees C) Add the potatoes and carrots to the roasting pan. Baste the lamb with beer, reserving the rest for basting at 20 minute intervals.
Continue to roast the lamb until the internal temperature reaches at least 140 degrees F (60 degrees C) for medium rare, about 1 1/2 hours longer. Remove from the oven and allow to rest for at least 5 minutes before carving. Spoon the pan drippings over the meat and vegetables when serving.