How to Make It
In a large pot, combine the water with the kosher salt, granulated and brown sugars, pink salt, pickling spice, mustard seeds and garlic. Cook over moderately high heat, stirring occasionally, until the salts and sugars have dissolved. Pour the brine into a large bowl and let cool, then refrigerate until chilled.
Using a metal skewer, poke holes all over the brisket. Pour the brine into a large roasting pan. Add the brisket and cover the pan with plastic wrap. Weigh the brisket down with heavy plates to keep it submerged in the brine and refrigerate. Let the brisket cure for 5 days, turning it once a day.
Remove the brisket from the brine and pat dry with paper towels. Place the brisket fat side up on a rack set on a rimmed baking sheet. Refrigerate, uncovered, for 24 hours.
Bring the brisket to room temperature. Light the grill, using about 50 charcoal briquettes. Soak the hardwood chips in water for 30 minutes. In a spice grinder, coarsely grind the peppercorns with the coriander seeds. Cover the fat side of the brisket with the peppercorn-coriander mixture.
Arrange the red-hot coals around the perimeter of the grill and set a double layer of heavy-duty foil in the center. Put an 8-inch aluminum pie plate on the foil and fill the plate halfway with water. Scatter about 1 cup of the drained hardwood chips over the hot coals. Set the grate on the grill and place the brisket, spiced side up, in the center. Cover and grill at 250°, partially vented, for about 5 hours. Every 45 minutes, replenish the hot coals and add 1 cup of the drained hardwood chips. The pastrami is done when an instant-read thermometer inserted in the thickest part registers 170°. Let the pastrami cool, then refrigerate until chilled.
Preheat the oven to 350°. Thinly slice the pastrami across the grain. Arrange the slices on a large rimmed baking sheet and drizzle about 1/2 cup of water on top. Cover tightly with foil and bake for about 20 minutes, until heated through. Serve warm or at room temperature.