1. Combine salt, sugar, and crushed garlic with 2 quarts water in large bowl or container; stir until salt and sugar dissolve. Prepare lamb as shown through illustration 4 (see below, Preparing the Lamb). Submerge lamb in brine, cover, and refrigerate for 2 hours.

2. While lamb brines, adjust oven rack to middle position and heat oven to 400°F. Place garlic heads cut side up on sheet of aluminum foil and drizzle with olive oil. Wrap foil tightly around garlic; place on baking sheet and roast until cloves are very soft and golden brown, 40 to 45 minutes. When cool enough to handle, squeeze garlic head to remove cloves from skins. Mash cloves into paste with side of chefs knife. Combine 2 tablespoons garlic paste and parsley in small bowl. (Reserve remaining paste for Roasted Garlic Jus, if making; see related recipe.)

3. Remove lamb from brine and pat dry with paper towels. Finish lamb preparation (illustrations 5 and 6). Season each roast with salt and pepper.

4. About 20 minutes before grilling, light large chimney starter filled with charcoal (6 qts, or about 100 briquettes) and burn until fully ignited, about 15 minutes. Empty coals into grill; build modified two-level fire by arranging coals to cover one-half of grill, piling them about 3 briquettes high. Position grill grate over coals, cover grill, and heat until hot, about 5 minutes; scrape grill grate clean with grill brush.

5. Grill lamb directly over fire until browned, 3 to 4 minutes; using tongs, rotate one-quarter turn and repeat until all sides are well browned, 12 to 16 minutes total. Move lamb to cooler side of grill, positioning roasts perpendicular to fire. Cover grill and cook 7 minutes for smaller roasts to 15 minutes for larger ones.

6. Remove cover; using tongs, rotate roasts 180°F so side facing fire now faces away. Replace cover and continue cooking until instant-read thermometer inserted into center of each roast registers 125°F for medium-rare or 130 to 135°F for medium to medium-well. (Roasting time will range from 6 to 15 minutes more depending on size of roasts; begin checking after 5 minutes and transfer each roast to platter as it reaches desired temperature.)

7. Transfer roasts to cutting board; tent loosely with foil and let rest 15 minutes. Remove twine; cut roast into 1/4-inch-thick slices and serve.

Serves 8 to 10