In a small bowl, mix together salt and sugar. Rub salt mixture all over pork belly, cover, and refrigerate up to 10 hours.
Preheat oven to 300 degrees.
Rinse brined pork to remove salt mixture and pat dry; transfer to a roasting pan. Roast pork until very tender, about 2 1/2 hours. Increase temperature to 450 degrees. Continue roasting pork until fat is golden, about 20 minutes more. Let cool for 30 minutes before transferring to a refrigerator until cold, about 1 hour.
Slice pork across the grain and return to baking dish with its juices. Cover and refrigerate until ready to serve, up to 3 days.
To serve, preheat oven to 350 degrees. Cover baking dish with parchment paper-lined aluminum foil; transfer to oven until warmed, 15 to 20 minutes. Brush hoisin sauce on the bottom half of each bun. Top with 2 to 3 slices of pork, cucumbers, and scallions. Serve immediately.
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