Mix the rub ingredients together. Apply liberally to the pork shoulder, pressing it gently into the meat until you’ve covered every side. Set any leftover rub aside for later. Place the pork shoulder in a large pot with a tight lid or a Dutch oven. Cover with a towel or lid and leave in the fridge for a few hours or overnight.
Pour enough water into the pot to cover the bottom. This will keep the juices from burning. Put the lid on and place the pot in a 200 F oven for 10 to 12 hours. I find it’s easier if I cook the pork overnight and pull it out in the morning, but you can put it in early in the morning and have it ready for dinner as well.
The supposed rule is that cooking takes 1.5 to 2 hours per pound of pork, but I find it usually takes a little longer than that. You are waiting for the internal temperature to reach 200 F. The meat is edible at 160 F, but at higher temperatures the tough connective tissues break down to create the flavor and texture.
If you don’t have a meat thermometer, poke the meat with a finger: when it’s so soft that it falls apart on its own, take it out of the oven.
To pull the meat, remove it from the juices and gently tear the pork apart with two forks or with your hands. Discard any larger bits of fat that you don’t wish to eat. If any section is hard to tear apart, the meat hasn’t cooked enough to break down the connective tissue. If you have the time to spare, put it back in the oven for another couple of hours.
Once you’ve pulled all of the pork, mix in any remaining rub and move it to a casserole dish or a large plate. If you aren’t eating the meat right away, stash it in the fridge.
Optionally, if you want to make a sauce from the pot full of drippings, bring it to a gentle boil on the stovetop over medium high heat. Let the juices thicken for 20 to 30 minutes. The fat will rise to the top: it’s the clear, thick layer, not the thin, red liquid below. Skim off as much of the fat as possible. Mix a few spoonfuls of the pan drippings with the pork before serving.
Feel free to add a little barbecue sauce to the pork if it isn’t flavorful enough for you.