Trim outer fat of brisket to 1/4 in. thick. If there's a thick pocket of fat in the meat, trim it out carefully, leaving about a 1/4-in. layer of fat.
Make brine: Whisk salt and water in a large bowl to dissolve, then whisk in remaining brine ingredients. "The bourbon adds flavor and helps tenderize the meat," says Holland. Add brisket and put a plate on top to submerge it. Chill overnight and up to 24 hours.
Soak hickory chunks in a bowl of warm water and applewood chunks in another, with a plate on top of each to submerge them, at least 45 minutes. Meanwhile, remove brisket from brine and pat almost dry.
Make rub: In an electric coffee or spice grinder, pulse white peppercorns until coarsely ground; pour into a bowl. "If you grind the spices right before you rub the meat, they'll taste a lot fresher." Repeat with coriander, then black peppercorns (because each spice has a different degree of hardness, they are best ground separately for the most even grind). Add both to bowl, along with brown sugar and salt; mix to blend. Rub generously all over brisket, including in the pocket and on the sides. "You have to really pack it on. If you have leftover rub, use it for pork chops." Let meat come to room temperature, about 1 hour.
Meanwhile, prepare a gas grill for indirect low heat: Set an aluminum drip pan (at least as large as brisket) under the cooking grate and on middle burner of a 3-burner grill or on one burner of a 2-burner grill. Fill drip pan halfway with hot tap water (it helps regulate the heat).
With grill lid open, ignite only exposed burner or burners and turn to medium (about 350°). Drain 4 soaked wood chunks (2 hickory, 2 applewood) and set directly on lit burners. "The applewood is soft and fruity and burns at a good rate. But hickory, that's the one you really taste. It's what people think about when they think about smoke." Close lid and heat 10 minutes, then adjust to maintain 250° to 300°. When smoke begins to billow from grill (it may take 20 minutes), position brisket on cooking rack over drip pan, fattiest side up. Close lid.
Cook and smoke brisket for 3 hours, setting 2 or 3 drained wood chunks directly on a lit burners every 30 minutes (you may not need all of them if enough wood remains to produce a consistently thick smoke). Turn brisket over halfway through smoking and add hot water to drip pan as needed to keep it about half full.
Preheat oven to 375°. Transfer brisket to a roasting pan just big enough to hold it. Pour in hot water to come halfway up brisket; cover tightly with foil. Braise, covered, until so tender that a fork slips in easily, about 3 hours.
Transfer brisket to a cutting board and let rest at least 20 minutes. Slice thinly against the grain and serve hot.
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Make ahead: Through step 7, up to 2 days. Let brisket cool 20 minutes, then wrap in foil and chill. When braising, increase time to about 3 1/2 hours. Also, save braising juices for reheating cooked brisket, covered, at 350°.