Season the pork with salt and pepper. Heat a large cast-iron casserole. Add the pork, fat side down, and cook over moderately high heat until browned all over, about 12 minutes total. Transfer to a plate. Add the tomato paste to the casserole and cook over moderately low heat, stirring, until deep red, 2 minutes. Add the paprika, cloves, allspice and brown sugar and cook until the sugar dissolves, about 30 seconds. Add the vinegar and bring to a boil, scraping up any browned bits. Add the molasses, ketchup, ground coffee and water and bring to a simmer.
Return the pork to the casserole. Cover and cook over low heat, turning the pork in the sauce occasionally, until very tender, about 4 hours. Transfer the pork to a large bowl; let rest for 30 minutes.
Meanwhile, skim the fat from the sauce. Boil the sauce over moderately high heat until thickened slightly, about 5 minutes. Using 2 forks, shred the pork; discard any large pieces of fat. Stir the shredded pork into the barbecue sauce. Mound the pork on the buns, top with coleslaw and serve.
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