Pre-heat oven to 300 degrees.
Remove the pork from the package, rinse and pat dry with paper towels.
Cut into 6 chunks and cover liberally with rub. Heat dutch oven (or other heavy bottom pot to medium heat.
Add oil, let heat for 2 minutes and then add the meat (the meat should sizzle when you add it.) Cook to get a nice crusty sear on the bottom, then continue to sear two more sides of the meat. You should be searing for about 10 minutes.
Once the meat is seared, add water, chicken broth and apple juice to the pot. You don’t want the meat to be submerged, but 2/3 of it should be covered. Put the lid on and place it in the oven. Bake for 3 hours.
Remove pork from the oven and use a slotted spoon to scoop out the meat. Place in a bowl and cover with foil.
While the meat is resting, start the sauce. To get the drippings (the liquid in the dutch oven for the sauce, I strain with a fine mesh strainer, and then put that into a fat separator. If you don’t have a separator, you can also scoop the fat settling on the top of the drippings. The point is not to add a bunch of fat to the sauce, just flavor.
Add the drippings, along with the rest of the sauce ingredients into a large pot and heat over medium high. Once the sauce starts to boil, turn the heat down to low and let reduce for about 30 minutes.
Once the sauce is done, place pork on a cutting board (it should be cooled by now) and shred.
Add the shredded meat to the sauce and mix to coat.
That’s it! Serve over a bed of cole slaw or on a bun!