The night before, prepare your roast:
Combine 3 tablespoons salt, 4 tablespoons of the brown sugar, all of the paprika and 1 teaspoon of cayenne in a small bowl. It should taste saltier than it is sweet, and have as much kick as you like, so add more if you wish.
If your pork shoulder has a thick fatty layer on one side, scoring can help prevent it from tightening the meat below as it shrinks. To score the fat, make shallow (1/8-inch deep) diagonal cuts in two directions a little under an inch apart in two directions, forming a diamond pattern.
Use your hands to pat the rub onto all sides of the pork — it’s going to be very thickly coated but don’t leave any rub behind. Place roast in a bowl or, if it fits in your fridge, the pan you’d like to roast it in tomorrow, cover with plastic wrap, and refrigerate for at least 6 hours or overnight.
Make your mop: Combine remaining 2 tablespoons brown sugar, all of the cider vinegar, ketchup, black pepper, and 1/3 cup water in a bowl and whisk until sugar dissolves. You want it to be pleasantly sharp (the fatty meat will cut right through any overpowering vinegar vibe) but not quite sour. I don’t find that I need salt, but you can add some if you wish. You’ll have a little over 1 2/3 cups.
Cook your pork: The next day, heat oven to 300 degrees F. Remove plastic wrap from pork and pour off any juices in the dish. If your pork is not in a roasting dish, transfer it to one. Cook pork for approximately 5 hours, or until it collapses, yielding easily when pulled back with a fork. After the first hour, add 1/4 cup mop to juices in pan and baste the meat with it. Continue to baste once an hour with juices that collect.
Make your slaw: Quarter, core, and thinly slice your cabbage. If slices are long, I cut them into 1 to 2-inch lengths, so the slaw doesn’t end up too cumbersome to pile on a sandwich. Place in a large bowl and pour 1/3 cup mop over, toss to combine. Add mayonnaise and mix well to combine. Season with salt and more pepper, if you wish, and taste, add more mop or mayo if needed. Refrigerate until ready to eat.
To finish and serve: Once meat is cooked, you can leave it at room temperature for up to an hour and a half. Rewarm briefly in a 450 degree oven. Shred pork into bite-sized pieces, discarding any larger chunks of fat, and pouring up to 1/2 cup of reserved mop over as needed to season and keep the meat moist.
Serve pulled pork on buns with slaw, seasoning with a splash of remaining mop and/or a barbecue sauce of you choice.
Note: I suspect you’re about to ask me if you can make this roast in a slow-cooker or InstantPot. Of course you can, but it will not be the same — it doesn’t get crisp or glossy. A slow-cooker can do this in 5 to 6 hours on high; an IP in about 80 minutes at high pressure, but neither will be varnished or crisp. You could blast it in a high-heat oven to create an edge, but it’s not going to be as astounding as the one took hours to form.