Chef Paul Steele of Phoenix Public Market Café makes his pulled pork by pre-roasting the pork in a flavorful dry rub, and then braising it until perfectly tender. Tossed in a smoky barbecue sauce and topped with coleslaw, it's a pretty remarkable version of the classic pulled pork sandwich.
Preheat the oven to 225 degrees.
In a small bowl, mix all of the seasonings together to make a dry rub. Reserve 3 tablespoons of the dry rub for the barbecue sauce, and coat the pork well with the rest. Place the pork on a baking sheet lined with foil or a large baking dish and slow cook in the oven until nice and golden brown, about 2 to 3 hours.
Remove the pork from the oven and increase the heat to 350 degrees. Pour the chicken stock into a large baking pan so that there's about an inch of liquid in the pan. Cut the roasted pork into 1-pound sized pieces, and place in the chicken stock. Cover the pan tightly with aluminum foil and cook until the pork is fork tender, about 3 hours.
While the pork is braising, make the barbecue sauce (recipe below). Remove from the oven and remove the pork from the braising liquid. Shred the pork, adding a bit of the braising liquid. Fold in the barbecue sauce at the end.
In a medium-sized saucepan, sweat the onions and the garlic in 1 tablespoon of oil. Add the dry ingredients and stir. Slowly add the wet ingredients, stirring constantly, and cook on medium-low until the sauce thickens, about 45 minutes.
For the coleslaw, combine all of the ingredients up to and including the caraway seeds. Mix well and season with salt and pepper, to taste.
Divide the pork evenly among brioche buns and top with coleslaw.