Combine paprika, brown sugar, salt, and pepper in a bowl and mix with a fork to create a seasoning rub.
Slice garlic into 8-10 thin slivers.
Make small slits in the pork roast and insert garlic slivers into the meat.
Rub the prepared seasoning mix all over the pork roast.
Place the seasoned pork roast into your crockpot or Instant Pot.
Pour Worcestershire sauce evenly over the pork roast.
For the slow cooker, cook on low for 5-6 hours or on high for 3-4 hours.
Check the doneness of the pork using a meat thermometer; the internal temperature should be between 195°F-205°F for easy shredding.
If not fully cooked, extend the cooking time by 30 minutes in a slow cooker or 10 minutes in the pressure cooker.
Once done, remove the bone and any excess fat from the pork.
Use two forks to shred the meat.
Stir in BBQ sauce to taste, mix well.
Assemble the pork between the buns or bread.
Add coleslaw if desired for extra crunch and flavor.