For the pulled pork: Mix the paprika, pepper, salt, chili powder, garlic powder and brown sugar in a bowl. Rub all over the pork. Cover and refrigerate for 1 hour or up to overnight.
Preheat the oven to 300 degrees F. Pour the beer into a roasting pan. Place the pork in the pan, cover with foil and bake until an instant-read thermometer inserted into the thickest part registers 170 degrees F, about 6 hours. Remove the pork from the oven and let the meat rest for at least 20 minutes.
Heat the barbeque sauce in a saucepan over low heat. Keep warm. Shred the pork using two forks. In a large bowl, toss the pork with the warm barbeque sauce until well coated.
For the coleslaw: Whisk together the mayonnaise, vinegar and granulated sugar in a large bowl. Add the cabbage and carrots and toss to coat. Season with salt and pepper, cover and refrigerate for at least 1 hour. The coleslaw can be made up to 2 hours in advance.
To serve, spoon the pulled pork mixture onto the bottom half of a brioche bun, and top with some coleslaw and the other bun half.
Recipe courtesy of Pablo Munoz