Prepare the barbecue for indirect cooking over medium heat (190°C to 230°C). If using a Weber® Q® barbecue, set up your barbecue with a convection tray and a trivet.
Using a sharp knife, cut 12 small slits into the flesh of the lamb. Push a piece of garlic into each slit. Drizzle the lamb with the oil, season with salt and pepper all over.
Roast the lamb over indirect medium heat, with the lid closed, for 40 minutes. While the lamb is roasting, make the mint sauce. In a medium bowl, combine the boiling water, salt and brown sugar, stirring until the salt and sugar has dissolved. Add the vinegar and the mint, stir to combine. Pour ¾ of the mint sauce into a serving dish and set aside until the lamb is ready to serve.
Once the lamb has cooked for 40 minutes, using a basting brush, brush the lamb with the ¼ portion of the reserved mint sauce. After a further 20 minutes, baste again with what remains of the ¼ portion of mint sauce. Continue roasting the lamb for a further 20 minutes or until the lamb has cooked through to your liking.
Once the lamb has cooked, leave to rest for at least 10 minutes before carving, to allow the juice to redistribute. Serve the lamb with the reserved mint sauce.
To estimate the cooking time, measure the meat through its thickest part and cook for 1 minute per millimetre for medium. For example, if the roast is 90mm thick, cook for 90 minutes.