Chop the Carrot (1).
Chop the Celery (1 stalk).
Dice or julienne the Yellow Onion (1).
Slice the Garlic (3 clove).
With a paper towel, pat the Bone-in Pork Shoulder (4 pound) dry, and begin trimming away any excess fat.
Season the pork shoulder liberally with Kosher Salt (to taste) and freshly ground Ground Black Pepper (to taste) on every side.
Heat a large pot over medium-high heat. When hot add the Grapeseed Oil (1 tablespoon). Place the pork shoulder in the pan to sear. Make sure there is plenty of room between the pork, so it can properly sear.
Turn the pork and evenly sear each side to a golden brown. When seared on each side, remove the pork shoulder and set aside, while you saute the aromatics.
Add the carrot, celery, onion and garlic to the pot and sauté for 5 minutes. Add the Fresh Thyme (3 sprig) with 2 minutes remaining.
Add the Chicken Stock (1 quart) and deglaze. Use a wooden spoon to scrape the fond (all those tasty bits of flavor on the pan) loose. Then add Barbecue Sauce (1/4 cup). Here we used Flaming Bacon Sauce.
Return the seared pork shoulder to the pan, and top with thyme. Place it in the oven and cook for 3 hours.
Combine the Mayonnaise (1 cup), Dijon Mustard (1 teaspoon), Lemon Juice (1 tablespoon) and Barbecue Sauce (1 1/2 tablespoon) to make the coleslaw dressing.
Add the dressing in batches to the Coleslaw Mix (1 package). You may not need all of it. You just want to coat the coleslaw, not drown it. Refrigerate while you wait for the pork to finish.
When the pork shoulder is finished, the bone will just fall out. Carefully remove the pork from the pan, and place it on a large plate. Tent aluminum over the plate, and let the pork rest for 15 to 20 minutes.
Shred the pork with two forks or with gloved hands. Toss with additional bbq sauce, if desired.
Serve your pulled pork on Slider Buns (2 package) with coleslaw and enjoy!