In addition to the ingredients, you will need 1 (13 x 9-inch) disposable aluminum roasting pan (if using charcoal) or 2 (8 1/2 x 6-inch) disposable aluminum pans (if using gas). Recipe from America’s Test Kitchen.
For the brisket and rub: Dissolve 2 cups salt and granulated sugar in 4 quarts cold water in large container. Slice brisket with grain into 1 1/2-inch-thick strips. Add brisket strips to brine, cover, and refrigerate for 2-4 hours. Remove brisket from brine and pat dry with paper towels.
Combine brown sugar, pepper, and remaining 1 tablespoon salt in bowl. Season brisket all over with rub. Just before grilling, soak wood chips in water for 15 minutes; drain. Using 2 large pieces of heavy-duty aluminum foil, wrap soaked chips in 2 foil packets and cut several vent holes in tops.
For a charcoal grill: Open bottom vent halfway and place disposable pan filled with 2 quarts water on 1 side of grill, with long side of pan facing center of grill. Arrange 3 quarts unlit charcoal briquettes on opposite side of grill and place 1 wood chip packet on coals. Light large chimney starter halfway filled with charcoal briquettes (3 quarts). When top coals are partially covered with ash, pour evenly over unlit coals and wood chip packet. Place remaining wood chip packet on lit coals. Set cooking grate in place, cover, and open lid vent halfway. Heat grill until hot and wood chips are smoking, about 5 minutes.
For a gas grill: Add 1/2 cup ice cubes to 1 wood chip packet. Remove cooking grate and place both wood chip packets directly on primary burner; place disposable pans each filled with 2 cups water directly on secondary burner(s). Set grate in place, turn all burners to high, cover, and heat grill until hot and wood chips are smoking, about 15 minutes. Leave primary burner on high and turn off other burner(s). (Adjust primary burner as needed to maintain grill temperature of 275 to 300 degrees.).
Clean and oil cooking grate. Arrange brisket on cooler side of grill as far from heat source as possible. Cover (positioning lid vent over brisket for charcoal) and cook without opening for 3 hours. Don’t be tempted to peek.
Adjust oven rack to middle position and heat oven to 275 degrees. Remove brisket from grill and transfer to rimmed baking sheet. Cover sheet tightly with foil. Roast until fork slips easily in and out of meat and meat registers about 210 degrees, about 2 hours. Remove from oven, leave covered, and let rest for 1 hour. Remove foil, transfer brisket to carving board, and pour accumulated juices into fat separator.
For the barbecue sauce: Combine ketchup, sugar, vinegar, Worcestershire, granulated garlic, cayenne, and 1/2 cup defatted brisket juices in medium saucepan. (Note: If you don’t have 1/2 cup of juices from the rested brisket, you can make up for the deficit using beef broth.) Bring to simmer over medium heat and cook until slightly thickened, about 5 minutes.
Cut brisket strips crosswise into 1- to 2-inch chunks. Combine brisket chunks and barbecue sauce in large bowl and toss to combine. Serve.