Place the pork belly in a casserole dish. Mix the salt and sugar in a small bowl and rub over the meat. Cover and refrigerate overnight.
Preheat oven to 400˚F. Remove the pork belly from the refrigerator and allow to come to room temperature. Discard any liquid that accumulated in the casserole dish. Put the pork belly on a wire sheet pan with a rack in the oven, fat side up, and cook for 1 hour, basting with the rendered fat in the bottom of the pan every 15 minutes, until golden brown. Turn the temperature down to 250˚F and cook for another hour, until the pork belly is tender but not falling apart. Remove from oven and let rest until room temperature. Once cooled, slice into ¼-inch-thick slices that are about 3 inches long.
Lay the lettuce leaves out on a large platter. Spoon a small a tablespoon of hoisin sauce and a slice of pork belly in each lettuce cup. Top with the kimchi, cucumber and garnish with green onion.
Enjoy with a glass of Cakebread Cellars Apple Barn Pinot Noir.