Food Network teaches how to crush, slice and mince garlic. Peel off some of the papery skin from the garlic and then smash the head of garlic with the heel of your hand to loosen the cloves; if you only need a few cloves, leave the head intact and pull some off. Separate the cloves. To peel a clove, cut away the root end with your knife. Lay the flat side of the knife over the clove while holding the knife handle, then with the heel of your free hand carefully whack the knife against the garlic to separate the skin from the clove. To crush the peeled garlic, lay the flat side of the knife over the clove and smash it again. To slice peeled garlic, lay the clove flat on the cutting board and hold it with the fingertips of one hand, keeping them curled under. Using a rocking motion with the knife, make thin slices by moving the knife slowly across the clove. To mince peeled garlic, lay the flat side of a knife over the clove and smash it. Roughly chop the clove then move your free hand flat across the tip of the knife and use a rocking motion to chop the garlic until it’s finely minced.
Mix the paprika, garlic power, brown sugar, dry mustard, and salt together in a small bowl. Rub the spice blend all over the pork and marinate for as long as you have time for, as little as 1 hour or up to overnight, covered, in the refrigerator.
Preheat the oven to 300 degrees F.
Put the pork in a roasting pan and bake for about 6 hours. Basically, roast the pork until it's falling apart and an instant-read thermometer inserted into the thickest part registers 170 degrees F.
To make the barbecue sauce: combine the vinegar, mustard, ketchup, brown sugar, garlic, salt, cayenne, and black pepper in a saucepan over medium heat. Simmer gently, stirring, for 10 minutes until the sugar dissolves.
Remove the pork roast from the oven and transfer to a large platter. Allow the meat to rest for about 10 minutes. While still warm, take 2 forks and "pull" the meat to form shreds. Using 2 forks, shred the pork by steadying the meat with 1 fork and pulling it away with the other. Put the shredded pork in a bowl. Pour 1/2 of the sauce on the shredded pork and mix well to coat.
To serve, spoon the pulled pork mixture onto the bottom 1/2 of the hamburger bun, and top with the spicy slaw. Serve with pickle spears and the remaining sauce on the side.
Combine the cabbage, carrot, red onion, green onions, and chile in a large bowl. In another bowl, mix the mayonnaise, mustard, vinegar, lemon juice, and sugar; stirring to incorporate. Pour the dressing over the cabbage mixture and toss gently to mix. Season the cole slaw with celery seed, hot sauce, salt, and pepper. Chill for 2 hours in refrigerator before serving.