Preheat oven to 250 F
Cut pork shoulder into large pieces, discarding any large pieces of fat and season with salt and pepper.
Heat cast iron pot on medium-high and add vegetable oil.
Working in batches, brown the chunks of meat on all sides.
Remove browned pieces of meat, add more oil if needed, and continue cooking until your meat has browned.
Remove all meat from the pot and add the beer, scraping up all the brown bits off the bottom of the pot.
After the alcohol from the beer has cooked off, add the apple cider vinegar, liquid smoke, spices, ¼ cup of beef broth, and add the meat back in the pot.
Put the lid on and move it to the oven. Cook for 2 ½-3 hours and check on it occasionaly, stirring the pot to make sure nothing sticks to the bottom and that it doesn't lose too much liquid. Scoop off any fat that seperates and floats to the top. If the liquid gets too low, add more beef broth.
After the meat has cooked completely, move pot back to the stove. Use a couple forks to pull it apart. Remove any pieces of fat that you want to eat.
Add BBQ sauce and stir to coat completely.