Make the slaw: remove the core from the cabbage and discard it; cut the cabbage into 8 chunks.
Finely chop the cabbage in a food processor using the metal blade and pulsing the motor (this is a chopped, not a sliced or slivered slaw); work in batches so as not to overcrowd the processor bowl.
Cut the bell pepper into the finest possible dice.
Add the mustard, mayonnaise, and sugar in a mixing bowl; whisk until smooth; whisk in the vinegar, celery seed, and black pepper; add in the chopped cabbage and diced bell pepper; stir to mix.
Taste for seasoning, add salt and more pepper if necessary; the slaw can be made up to 1 day ahead.
Make the pork: generously season the pork all over with salt and pepper.
Set up grill for indirect grilling and preheat to medium (to be strictly authentic, you’d use charcoal; but can be made on a gas grill; if using charcoal grill, place a large drip pan in the center).
When ready to cook, place the pork skin side up, if there is one, in the center of the hot grate, over the drip pan and away from the heat; cover the grill.
Cook the pork until very tender, 4-5 hours; to test for doneness, use an instant-read meat thermometer; internal temperature should be about 195° (the cooking time will depend on the size of the Boston Butt and the heat of the grill).
If the pork starts to brown too much, cover it loosely with foil; if using a charcoal grill, every hour you will need to add 12 fresh coals to each side.
Transfer the cooked pork to a cutting board, cover it loosely with foil; let rest for 10 minutes.
Pull off the brown skin and finely chop it with a cleaver (these crispy bits are called brownies and they’re indispensable for a proper Memphis pork sandwich).
Pull the pork into large pieces, discarding any bones or lumps of fat (wear gloves when doing this).
Using your fingertips or a fork, pull each piece of pork into thin shreds; or use a cleaver to finely chop it.
To serve: pile the pulled pork and brownies on the hamburger buns; top each with a mound of mustard slaw and, if desired, a dollop of barbecue sauce; serve.