Prepare the pork: Combine the mustard, honey, 1 teaspoon salt, 1 tablespoon pepper, the paprika and garlic in a bowl. Prick the pork on all sides (including the fat) with a paring knife, about 1/2 inch deep. Brush all over with the mustard mixture. Tightly wrap with plastic wrap and refrigerate at least 6 hours.

Unwrap the pork, place in a roasting pan and bring to room temperature. Meanwhile, preheat the oven to 250 degrees F.

Transfer the pork to the oven and pour 1 inch hot water into the pan. Cook 3 hours, adding water as needed to maintain 1 inch.

Remove the pan from the oven, add water if needed and cover tightly with foil. Return to the oven and cook 6 more hours. Turn off the oven and let the pork rest inside, about 1 hour.

Meanwhile, make the sauce: Melt the butter with the oil in a large skillet over medium heat. Add the onions, season with salt and pepper and cook, stirring occasionally, until tender, 6 to 8 minutes. Add the garlic and paprika and cook 2 to 3 more minutes (reduce the heat if the garlic starts to brown). Stir in the brown sugar, preserves, ketchup and chili sauce, stirring after each addition. Bring to a simmer, then stir in the vinegar. Add salt to taste.

Remove the pork from the oven and take the meat off the bone. Coarsely shred the meat using 2 carving forks. Toss with some of the barbecue sauce and pan juices and season with salt and pepper. Serve on rolls with coleslaw.

Photograph by Steve Giralt