Mix the brown sugar, salt, pepper, five-spice powder, garlic powder, ground ginger and onion powder in a bowl, and then rub all over the pork. Place on a wire-racked baking sheet. Cover with plastic wrap and let it sit for 2 hours, or preferably overnight in the refrigerator.
Preheat the oven to 325 degrees F with the oven rack in the middle position.
Remove the plastic wrap and cover the pork with a layer of parchment paper. Then seal over the top with aluminum foil. Roast for 3 hours. Remove, uncover and drain any liquid fat. Return the pork to the oven and roast until the pork registers 200 degrees F on an instant-read thermometer and the pork is well browned, about 1 1/2 hours more. Transfer the pork to a large dish, cover with foil and let rest for 20 minutes.
Sandwich Build: Using two forks or your hands, pull apart the warm pork into shreds and chunks. Butter and griddle the rolls until golden brown. Place ample quantities of pork on the bottom buns, then top with Pickled Cukes and Carrots and Sweet-and-Hot Mustard Sauce or Sweet Chile Sauce if desired.
Pickled Cukes and Carrots:
Bring 1 cup water, the vinegar, sugar and salt to a boil in a saucepan until the sugar and salt are dissolved. Take off the heat, and add in the carrots, cucumbers and crushed red pepper and let sit for at least 30 minutes.
Sweet and Hot Honey Hot Mustard:
Mix the mustard, water, honey, sesame oil, vegetable oil and salt in a bowl until smooth.
Sweet Chile Sauce:
Bring the vinegar, sugar and salt to a boil in a saucepan and cook until dissolved. Simmer until thickened and reduced by half, about 15 minutes. Stir in the crushed red pepper, ginger and garlic, and serve.