Step 1

For the spice rub and beef: Combine salt, pepper, and cayenne in small bowl. Following photo 1, quarter roast and remove excess fat and gristle. Rub meat all over with salt mixture and transfer to large disposable aluminum roasting pan. (Salt-rubbed meat can be wrapped tightly in plastic and refrigerated for 24 hours.)

Step 2

Seal soaked wood chips in foil packet and cut vent holes in top. Open bottom vent on grill. Light 50 coals; when covered with fine gray ash, pour in pile on one side of grill. Arrange foil packet directly on coals. Set cooking grate in place and heat, covered, with lid vent open halfway, until wood chips begin to smoke heavily, about 5 minutes. (For gas grill, place foil packet directly on primary burner. Heat all burners on high, covered, until wood chips begin to smoke heavily, about 15 minutes. Leave primary burner on high and shut other burner[s] off.) Arrange roasting pan with beef on cooler side of grill and barbecue, covered, until meat is deep red and smoky, about 2 hours.

Step 3

Adjust oven rack to lower-middle position and heat oven to 300 degrees. Following photo 3, flip meat over, cover pan tightly with foil, and bake until fork inserted into meat can be removed with no resistance, 2 to 3 hours. Transfer meat to large bowl, tent with foil, and let rest 30 minutes. While meat rests, skim fat from accumulated juices in pan; reserve 2 tablespoons fat. Strain defatted juices; reserve 1/2 cup juice.

Step 4

For the barbecue sauce and to finish: Combine onion and reserved fat in saucepan and cook over medium heat until onion has softened, about 10 minutes. Add garlic and chili powder and cook until fragrant, about 30 seconds. Stir in remaining ingredients and reserved meat juices and simmer until thickened, about 15 minutes. Using 2 forks, pull meat into shreds, discarding any excess fat or gristle. Toss meat with 1/2 cup barbecue sauce. Serve, passing remaining sauce at table.