Make the pork: Mix 2 teaspoons salt and the brown sugar in a bowl. Rub the pork with the brown sugar mixture. Cover with plastic wrap and refrigerate at least 4 hours, or overnight.
Make the sauce: Heat the vegetable oil in a saucepan over medium heat. Add the onion and cook until soft, about 5 minutes. Add the garlic, ginger and red pepper flakes and cook, stirring, 2 more minutes. Add the ketchup, apple juice, oyster sauce, vinegar, mustard powder and 1/4 teaspoon salt. Bring to a simmer and cook, stirring occasionally, until the sauce is thickened, about 20 minutes. Let cool 15 minutes, then transfer to a blender and puree until smooth. Set aside about one-quarter of the sauce for serving.
Remove the pork belly from the refrigerator about 30 minutes before grilling. Preheat a grill to medium, then prepare for indirect heat: For gas, turn off the burners on one side. For charcoal, push the coals to one side. Place a drip pan under the grates on the cooler side of the grill.
Brush the grill grates with vegetable oil. Place the pork on the cooler side of the grill (indirect heat) and cook, turning occasionally, until fork-tender but not falling apart, 2 hours, 30 minutes to 3 hours, brushing with the sauce occasionally during the last hour of cooking. Move the pork to the hotter side of the grill (direct heat) and cook, turning and brushing with more sauce, until glazed and lightly charred, about 5 more minutes. Transfer to a cutting board and let rest 20 minutes. Slice the pork belly and serve with the cornbread and reserved sauce.