Step 1: Make the brine: Place the coarse salt, sugar, pickling spice, curing salt, garlic, and tap water in a large nonreactive pot. Bring to a boil over high heat and continue boiling until the salts and sugar are completely dissolved, stirring from time to time, 3 minutes. Remove from the heat and add the ice water. Let cool completely.
Step 2: Meanwhile, trim the pork, removing any skin, sinew, or blood spots. Place it in a large heavy-duty resealable plastic bag or a nonreactive baking dish. Add the brine, squeeze out the air, and seal the bag, or cover the baking dish with plastic wrap. Place the bag in a roasting pan to contain any leaks. Brine the pork in the refrigerator for 5 days, turning it over daily so it brines evenly.
Step 3: Make the rub: Place the peppercorns and coriander seeds in a dry cast-iron skillet and toast over medium heat until fragrant, about 3 minutes, shaking the pan so the spices toast evenly. Transfer the spices to a bowl and let cool, then coarsely grind in a spice mill. Work in batches if your spice mill is small.
Step 4: Drain the pork, discarding the brine. Rinse well, drain again, and blot dry with paper towels. Place the pork on a rimmed baking sheet. Sprinkle with the rub on all sides, rubbing the spices into the meat with your fingertips so that it’s thickly and thoroughly crusted. You can smoke the pork right away, but you’ll get even more flavor if you let it rest in the refrigerator overnight.
Step 5: Set up your smoker following the manufacturer’s instructions and preheat to 225ºF. Add the wood as specified by the manufacturer.
Step 6: Place the pork fat side up (if the meat has a fat cap) in the smoker. Smoke until the meat is cooked and tender and the internal temperature reaches 160ºF. This will take 4 to 5 hours. Transfer the pork to a rimmed baking sheet and let cool to room temperature, then cover with plastic wrap and refrigerate until completely chilled.
Step 7: To serve, slice the pork pastrami across the grain as thinly as possible. Eat the first few slices with your hands. Then make the difficult decision, the one where you decide if rye bread and mustard would be an enhancement or a distraction.
Use in Pork Pastrami Hash.