Preheat the oven to 225 degrees F. Set the pork on a cutting board and score the fat in a crosshatch pattern, making the cuts about 3/4 inch deep and 1 inch apart. Make the rub: Combine the pimenton, garlic powder, cayenne pepper, brown sugar, celery salt, mustard powder and 1 1/2 teaspoons salt in a small bowl. Massage it into the meat.
Place the pork in a roasting pan and pour the beer into the pan. Cover with foil and roast 3 hours. Check it periodically to make sure everything is going along just fine, and turn the roast over every hour.
Remove the foil and continue roasting until the pork has reached an internal temperature of 190 degrees F, about 1 1/2 more hours. Remove from the oven, cover loosely with foil and let rest 30 minutes.
Sometime during the marathon cooking time, make the sauce: Combine the vinegar, garlic, chile, brown sugar, tomato paste, dijon mustard and 1 1/2 teaspoons salt in a small saucepan and bring to a boil. Taste it to make sure it is delicious; set aside. Remove the chile. When the sauce is cool, I recommend putting it in a squeeze bottle for easy use.
Pull the pork into long shreds using 2 forks. Get rid of the fat and anything else that doesn't look delicious. Toss the pork with any residual pan juices and add salt to taste.
Serve the pork on slider rolls with a drizzle of sauce; top with coleslaw.
Photograph by Charles Masters
Recipe courtesy of Anne Burrell for Food Network Magazine