Score the skin of the pork by slicing a crosshatch pattern through the skin down to the meat.
In a large bowl, combine one cup of the soy sauce, sugar, garlic, and green onions. Add the pork and toss to coat evenly; marinate for at least one hour.
Preheat the oven to 275 degree F.
On a baking sheet, place the asparagus halves to the right and diced potatoes to the left. Toss the vegetables with the oil, salt, and pepper. Place the marinated pork in the middle of the baking sheet. Bake one to one and a half hours, depending on the weight of the pork.
Increase the heat of the oven to 500 degree F.
In a small bowl, combine the brown sugar, honey, and remaining soy sauce, stirring until smooth.
Spoon the honey glaze over the top of the pork, making sure to fill the cracks and crevices on top. Bake for another 15-20 minutes or until sugar is dark brown and caramelized, and the top of the pork is crispy.
Remove the vegetables and pork from the tray, making sure to save all the juices.
Slice the pork into ½-inch slices, and plate with the roasted vegetables. Spoon the reserved pan juices on top of the pork, and enjoy!