Preheat the oven to 350 degrees F. Take the pork out of the refrigerator 45 minutes before you are ready to roast to allow the pork to come to temperature.
Place the pork into a roasting pan fitted with a rack or onto a baking sheet, fat side up, and season with salt and pepper. Put in the oven and roast for 1 hour. Meanwhile, make the glaze.
In a saucepan over medium-high heat, bring the apple juice to a boil and reduce it by half, about 10 minutes. Whisk in the brown sugar, soy sauce, Worcestershire sauce, and mustard and simmer until thickened, another 5 to 7 minutes.
After the pork has roasted for 1 hour, start brushing it with the glaze every 15 minutes. Cook until the roast reaches an internal temperature of 150 degrees F, about 2 hours total cook time. Remove from the oven, give it another coating of glaze, and let it rest, uncovered, for 15 minutes before carving. (Reserve 1 cup of the meat for the Round 2 Recipe Pork Hash).