Preheat oven to 325°F.
Combine rub ingredients and sprinkle and pat all sides of the butt with the dry rub. Heat the oil in a Dutch oven. When the oil is hot, add the butt and sear on all sides until there is nice browning. Once all sides are browned, remove the meat, add the chicken stock and deglaze the pan by scraping up all the charred bits with a wooden spoon.
Return the meat to the pan, fat-side up and cover. Transfer to the oven and cook for about an hour per pound. All ovens are different so start checking after 4 or 5 hours for an internal temp of 145°F.
Carefully take the meat out of the pot, it will start falling apart. Put it on a cutting board and use two forks to pull apart the roast while it is hot—it will shred more easily. Discard what is left of the fat cap, the meat should easily shred, discard the bone and any other fatty pieces. Put the shredded pork into a chafing dish to keep warm. Some of the reserve liquid can be used to flavor it but it will have a very intense taste of the dry rub. Use it sparingly.
For Carnitas, place all of ingredients for the Chipotle Sauce into a food processor and blend until smooth. Make ahead of time for all the flavors to meld. Drizzle over pork tacos.
For the Carolina Mustard Sauce, melt butter in a saucepot. Add the minced shallots and cook until soft. Add all the other ingredients and cook until honey and sugar dissolve.
Let rest for flavors to meld then serve room temperature or reheat to serve warm. Pour over pulled pork on a Hawaiian bun with some bread-and-butter pickle chips.