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1
Make the slaw: remove the core from the cabbage and discard it; cut the cabbage into 8 chunks.
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2
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.
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3
Cut the bell pepper into the finest possible dice.
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4
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.
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5
Taste for seasoning, add salt and more pepper if necessary; the slaw can be made up to 1 day ahead.
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6
Make the pork: generously season the pork all over with salt and pepper.
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7
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).
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8
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.
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9
Cook the pork until very tender, 4-5 hours; to test for doneness, use an instant-read meat thermometer; internal temperature should be about 195u00b0 (the cooking time will depend on the size of the Boston Butt and the heat of the grill).
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10
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.
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11
Transfer the cooked pork to a cutting board, cover it loosely with foil; let rest for 10 minutes.
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12
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).
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13
Pull the pork into large pieces, discarding any bones or lumps of fat (wear gloves when doing this).
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14
Using your fingertips or a fork, pull each piece of pork into thin shreds; or use a cleaver to finely chop it.
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15
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.
