Preheat the oven to 300 degrees F. In large bowl, mix together the pork butt and sauce. Transfer the pork mixture to an 8- by 8- by 2 -inch pan. Cover tightly with foil and bake until very hot, about 1 hour. Divide the mixture on the hamburger buns and serve immediately.
Preheat the oven to 275 degrees F.
In a food processor, combine the peppercorns, garlic, and cloves and puree. While the motor is running, drizzle in the oil until a paste is formed. Using a rubber spatula, scrap the garlic paste into a small bowl.
Place the pork butt on a work surface and season all over generously with salt. Rub all over with the garlic paste. Place in an oven-safe roasting bag and close with a twist tie. Place in a large roasting pan, and cook until tender, about 5 hours.
Remove roast from the oven. Slip the oven-roasting bag off the meat and discard. Transfer the cooking liquid to a medium saucepan. Skim the fat from the cooking liquid with a ladle or de-greaser. Bring to a boil, lower the heat, and simmer to thicken the juices slightly.
Raise the oven to 400 degrees F. Return the pork, in the roasting pan, to the oven. Continue roasting, basting frequently with the simmering cooking liquid, until well-browned, about 30 minutes. If there is any cooking liquid left, pour it over the pork.
Remove pork from the oven and let it rest at room temperature for 10 minutes. With the pork drippings you may make a vinegar sauce using this formula: for every 1/2 cup of drippings, whisk with 3 tablespoons vinegar and 1/4 teaspoon salt. Either carve the pork into thin slices, or, using 2 forks, pull into small pieces. Serve with the vinegar sauce on the side.
Heat the oil in a medium saucepan over medium-high heat. Add the onion and cook, stirring, until lightly browned, about 4 minutes. Add the garlic and crushed pepper and cook, stirring frequently, until fragrant, about 45 seconds. Add the tomato paste and cook, stirring, until lightly browned, about 1 minute more.
Add the tomatoes, vinegar, sugar, and salt and bring to a boil. Lower the heat, and simmer, uncovered, stirring occasionally, until deep red in color and reduced to about 4 cups, about 25 minutes. Season with pepper to taste. Use now, or store, covered in the refrigerator for up to 3 days or freeze for up to 1 month.
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