Step 1: Combine the water, salt, brown sugar, whiskey, pickling spice, and curing salt in a large nonreactive container. Bring to a boil on the stovetop over medium-high heat. Let cool to room temperature. Add the brisket. Cover and refrigerate for 3 days, turning the meat twice daily. (Weight the meat to keep it submerged in the brine with a bag of ice or a heavy plate.)
Step 2: Drain the brisket and discard the brine. Soak the meat in cold fresh water, then drain again.
Step 3: When ready to cook, set up a charcoal grill or smoker for indirect grilling and preheat to 250 degrees F. Toss 1-1/2 cups of wood chips on the coals.
Step 4: Place the brisket fat-side down on the grill grate and smoke the meat until the internal temperature reaches 180 degrees F, about 5 hours, replenishing the charcoal and smoking chips as needed. Wrap the meat in butcher paper and continue smoking 1 hour more, or until the internal temperature reaches 195 degrees.
Step 5: Place the corned beef in its butcher paper in an insulated cooler and let rest 1 hour. Transfer to a cutting board and slice the meat against the grain into 1/4-inch slices. Serve with barbecued cabbage.
Curing salt, also known as pink salt, Prague powder, or Insta-Cure #1, can be purchased online or from retailers who carry sausage-making supplies. While not strictly necessary, it gives corned beef its traditional pink color.