In a small bowl, mix paprika, brown sugar, onion powder, garlic powder, cayenne pepper, and black pepper. Set aside
Pat pork shoulder dry on both sides, and put into a container or on a dish. Season both sides of the pork with the sugar mixture. Put pork into the fridge, uncovered, for 2-3 hours.
Remove pork from the fridge, and season both sides of pork with salt.
In a crockpot, or oven safe dish, add garlic, onion, cider, liquid smoke, water, bay leaf and thyme. Place pork into liquid.
Crockpot - Cook on high for 2 hours, or on low for 4 hours. Oven - Cover and bake at 350 degrees for 2 hours.
Once cooked, remove pork from the liquid into a large bowl and let cool for about 5 minutes. Reserve 1/4 cup of the braising liquid. Shred the pork, removing any bone, gristle, and tendons. Fat can be removed to your liking.
Optional: Remove the sliced onions and the garlic cloves from the braising liquid. Roughly chop and add with the shredded pork.
Add bbq sauce to the pork, along with reserved braising liquid. Mix to combine.