1. Soak 2 cups wood chips in water to cover for 30 minutes; drain. Place chips in small disposable aluminum pan; set pan on primary burner (burner that will remain on during barbecuing); position cooking grate. Ignite grill, turn all burners to high, cover, and heat until very hot and chips are smoking, about 15 minutes. (If chips ignite, use waterfilled spray bottle to extinguish.) Scrape grate clean with grill brush. Turn off all burners except primary burner.

2. Meanwhile, sprinkle both sides of chicken legs with salt and pepper. Place chicken legs skin side up in single layer on cool side of grill. Cover and cook 35 minutes (internal grill temperature should register about 325°F after 30 minutes).

3. Working quickly to prevent excess heat loss, remove cover, and using tongs, rotate each leg so that side formerly facing burner now faces away (do not flip chicken): cover and cook until instant-read thermometer inserted into thickest part of thighs registers about 185°F, 35 to 45 minutes longer (internal grill temperature should register about 310°F). Transfer chicken to cutting board; let rest until cool enough to handle.

4. FOR THE SAUCE: While chicken is cooking or cooling, process onion and water in food processor fitted with steel blade until puréed and mixture resembles slush, about 30 seconds. Pass mixture through fine-mesh strainer into liquid measuring cup, pressing on solids with rubber spatula; you should have 3/4 cup strained onion purée. Discard solids in strainer.

5. Whisk onion purée, ketchup, apple cider, Worcestershire, mustard, molasses, pepper, and 3 tablespoons cider vinegar together in medium bowl. Heat oil in large nonreactive saucepan over medium heat until shimmering; add garlic, chili powder, and cayenne and cook until fragrant, about 30 seconds. Stir in ketchup mixture; increase heat to medium-high, bring to boil, reduce heat to medium-low, and simmer, uncovered, until flavors meld and sauce is slightly thickened, about 15 minutes. You should have scant 4 cups sauce. Transfer about 2 cups sauce to serving bowl; leave remaining sauce in saucepan.

6. Remove and discard skin from chicken legs. Using fingers, pull meat off bones, separating larger pieces (which should fall off bones easily) from smaller, drier pieces into two equal piles.

7. Place smaller chicken pieces in food processor and pulse until just coarsely chopped, three to four 1-second pulses, stirring chicken with rubber spatula after each pulse. Transfer chicken to sauce in saucepan. Using fingers or two forks, pull larger chicken pieces into long shreds and add to saucepan. Stir in remaining tablespoon cider vinegar; cover saucepan and heat chicken over medium-low heat, stirring occasionally, until heated through, about 10 minutes. Add hot sauce to taste and serve, passing remaining barbecue sauce separately.

Serves 6 to 8