Roughly chop the garlic cloves in a small food processor. Add the mint and repeat. Add the brown sugar, salt, pepper, mustard, and oil, and blend to a paste. Spread the paste evenly on the meat side of the roast. Roll the leg into a roast shape and tie with cotton butcher's twine.
Fire 2 quarts (1 chimney's worth) of charcoal (natural chunk is best). When charcoal is lightly covered with gray ash, split the coals into 2 piles and move them to the far sides of the cooker. Close the lid and allow the grate to heat.
When the grill is nice and hot, grease the grates with oil using a kitchen towel and tongs. Then, place the lamb, skin-side up, on the middle of the hot grate. Add the rosemary sprigs to the charcoal briquettes and close the lid and grill. After 20 minutes, flip the roast and rotate it 180 degrees. Insert a probe thermometer into the roast and continue to grill until it reaches an internal temperature of 135ºF, 25 to 30 minutes.
When the roast reaches 135ºF, remove it from the heat. Remove the butcher's twine from the roast. Cover with foil and rest it for 15 minutes before slicing and serving.