Prep Pork: Trim off some of the excess fat from the pork shoulder.
Sear Pork: Heat oil in a large skillet on medium-high and then add the pork shoulder. Sear on high for about 2-3 minutes on all sides.
Slow Cook: Add seared pork shoulder to the crock pot and pour over BBQ sauce. Cook on high for 5-6 hours or on low for 8-10 hrs until pork it fork tender and the internal temp is at least 195℉.
Make Slaw: Add shredded cabbage and carrot to a bowl and mix. Add mayo, vinegar, lemon juice, sugar, salt, and pepper to a small bowl and mix well, and then add to the cabbage and carrot. Mix well so that it all is well combined.
Shred Pork: When the pork is done, use two forks to shred the pork in the crock pot. Mix well with the sauce/liquid.
Enjoy: Create the sandwiches by adding pulled pork and slaw to a homemade brioche bun and enjoy!