Prepare the rub by combining the paprika, salt, sugar, mustard, cumin, pepper, garlic and onion powders and cayenne in a small bowl. Trim any large pieces of exterior fat from the pork if desired. Pat the rub mixture on all sides of the pork and place uncovered, in a dutch oven. Roast uncovered for 1 hour.
Remove the pork from the oven, brush with the olive oil, add the water, cover and return to the oven for approximately 5 hours longer. At this point the pork should be very tender and pull apart easily with a fork. Total roasting time runs between 90 and 100 minutes per pound.
Transfer the pork to a large platter and allow to cool enough to handle. With two dinner forks, shred the meat into bite-sized pieces, removing any large chunks of fat in the process.
Prepare the barbecue sauce:
Combine all the ingredients in a small saucepan and heat to a simmer over medium heat. Cook for about 15 to 20 minutes until thickened.
Add the barbecue sauce to the shredded pork.
Assemble the sandwiches:
Fill each bun with a portion of shredded pork and top with a tablespoon or two of coleslaw (recipe follows).
Serve with a dill pickle and a side of chips.
Tips for Making This Recipe
You can freeze the leftover pork in airtight containers. It will keep for up to 6 weeks in the coldest part of the freezer.
Slow Cooker Instructions:
You can cook the pork in a slow cooker instead of the oven if desired. Simply add a layer of sliced onion to the bottom of the cooker, put the rub-coated pork on top and add the water. Cover and cook on low for 8 to 10 hours (depending on the size of your roast), or until the pork is tender and pulls apart easily with a fork.