Step 1In a mortar and pestle or food processor, mince the garlic. Add the rosemary, olive oil and salt and grind or process to a thick paste. Add the yogurt and mix well.
Step 2Place the lamb in a 1-gallon resealable plastic bag and pour in the yogurt mixture. Squeeze out any air and seal the bag tightly. Rub through the bag to make sure the yogurt covers as much of the lamb as possible. Refrigerate overnight.
Step 3The next day, start a fire with 10 pounds of charcoal. Remove the lamb from the bag and wipe off any excess marinade. Skewer the lamb on the spit and secure it tightly.
Step 4When the coals are covered in gray ash and the fire has settled to the point that you can hold your hand at skewer level for 3 to 4 seconds, begin roasting the lamb over indirect heat. It will take about 1 1/2 hours to reach 130 degrees, which is slightly on the medium side of medium-rare. When sliced, the lamb will be pink and moist but the fibers will be set and tender.
Step 5Remove the lamb to a platter and set aside for 10 minutes to finish cooking and to allow the juices to redistribute. Remove the lamb from the spit, slice one-half- to three-quarters-inch thick and serve along with its juices.