For the rub: Mix the paprika, 1 tablespoon each of salt and black pepper, the brown sugar, and the cayenne. Rub spice mixture all over brisket, wrap tightly, and refrigerate overnight.
Soak the wood chips in water for at least 30 minutes before grilling. Prepare an outdoor grill with a medium to medium-low fire for indirect grilling.
For the sauce: Mix the tomato puree, beer, celery, onion, 1/2 cup of the vinegar, the brown sugar, mustard, bacon, garlic, chiles, bay leaves, chili powder, 1 tablespoon salt, and black pepper to taste in a large disposable aluminum pan. Put brisket in the sauce.
Throw a handful of drained wood chips on the hot coals, put the pan over the cooler side of the grill, and cover so the vent holes are directly over the brisket. Baste meat every 30 minutes, turning occasionally and adding water to the pan as necessary to keep meat partially submerged, until the meat is tender and an instant-read thermometer inserted in the thickest part registers 200 degrees F, about 3 3/4 hours. Replenish the charcoal as needed to maintain a medium to medium-low fire.
Transfer the brisket to a cutting board, tent with foil, and let rest for 20 minutes. Skim the fat from the braising sauce and stir in the remaining 1/4 cup cider vinegar and salt to taste. Reheat if necessary. Thinly slice brisket across the grain and arrange on a serving platter. Spoon some sauce over the meat and pass the rest at the table.
There are lots of wood chips to choose from. We like the stronger, traditional flavor that hickory or mesquite gives to this dish. Fruit woods such as apple and cherry are delicious with milder meats, such as pork, poultry, or fish. Chips also come in different sizes-either chunks or bits. The chunks don't require soaking and produce a big blast of fast-burning smoke. The bits, which do require soaking, produce smoldering smoke.
From Food Network Kitchens Get Grilling, Meredith, 2005