Heat the olive oil in a medium-sized saucepan over high heat. Add in garlic and onion and cook until just tender and fragrant, about five minutes.
Add in apple butter, apple cider vinegar, honey, water, paprika, mustard, salt, worcestershire sauce, and chili sauce. Bring to a boil, reduce heat and simmer until thickness of a barbecue sauce (about 15 minutes). Reserve about one cup of the sauce for serving.
Place shoulder roast in large slow cooker, cover with remaining barbecue sauce, and cook on low for 8-10 hours, or high for 6-8 hours (or until the pork is tender enough to shred)
Shred pork with two forks. To serve, pile on top of buns, then drizzle with reserved barbecue sauce and top with slaw.