When ready to cook, start the Traeger grill on smoke with lid open until fire is established (4 to 5 minutes). Set the temperature to High and preheat, lid closed, for 10 to 15 minutes.
Thread garlic onto skewer. Grill garlic, tomatillos, onion quarters, and chiles until dark brown spots form on all sides, about 9 minutes for onion, 6 minutes for tomatillos and chilies, and 4 minutes for garlic.
Remove everything from grill and place the chiles directly into a ziplock bag. Allow chiles to steam in bag for 15 minutes. Place a cast iron pan on grill, close lid and allow to preheat for 10 minutes.
Peel garlic and remove skin from chiles. Coarsely chop the onion, chiles, and garlic. Transfer tomatillos, cappers and all vegetables into blender. Add cilantro and 1/2 teaspoon sugar. Puree until smooth. Season to taste with kosher salt.
Add oil to preheated cast iron pan. Carefully add the tomatillo mixture and stir until slightly thickened, stirring often (about 2 minutes). Add broth and 2 tablespoons lime juice.
Close lid and allow mixture to reduce until it measures about 2 1/2 cups (about 15-20 minutes). Season the verde to taste with salt and more sugar and lime juice. Cool slightly, then cover and chill. Remove from grill and turn temperature dial to Smoke setting.
Pat lamb dry and score fat by making shallow cuts all over with tip of a sharp small knife. Using a paring knife, make little incisions all over lamb and stuff with garlic cloves. Rub olive oil over lamb and liberally season with salt, pepper and rosemary. Let stand at room temperature for 30 minutes.
Place leg of lamb in center of grill. Smoke lamb on the Smoke setting for 30 minutes.
Increase temperature 350 degrees F and cook until a thermometer inserted into the thickest part of the meat registers 130 degrees F (about 1-1/2 hours).
Transfer to a cutting board and let stand 15 to 25 minutes; the internal temperature will rise to 140 degrees F for medium-rare.
Slice and serve with salsa verde. Enjoy!