Have plenty of napkins on hand — although you might prefer not to use them. These ribs are truly finger-lickin’ good. (Note that the ribs need to be started about a day in advance of serving.)
Preheat the oven to 250 degrees.
Meanwhile, from the back, boney side of the ribs, slide a thin, blunt tool, such as a flathead screwdriver, over the bone but under the thin membrane that covers the entire back of the rack. Work the tool down the bone, swaying from side to side, until there’s a gap large enough for you to grab the membrane and peel it off. Place the ribs in a large roasting pan (you can cut the racks into pieces if need be). Set aside.
In a medium saucepan over medium-high heat, combine the aji-mirin, soy sauce, vinegar, sesame oil, Chinese five-spice powder, and garlic and bring to a boil. Pour the hot mixture over the ribs, cover with a tight-fitting lid, and bake until the meat is tender and almost falling off the bones, about 2 hours. Remove from the oven and let the ribs cool in the sauce. Refrigerate for 12-24 hours.
Remove the ribs from the baking liquid (save the liquid), scraping the fat off the ribs. Cut each rack into 3-rib pieces and set aside. Skim the fat off the top of the liquid. Strain 1 ½ cups of the liquid and set aside (discard the remaining liquid).
In a medium saucepan over medium heat, combine the strained baking liquid with the brown sugar and the cornstarch mixture, whisking to dissolve the sugar. Bring to a boil, stirring, until thickened, 1-2 minutes. Remove from the heat and set aside.
Prepare the grill to medium heat and lightly oil the grate. Grill the ribs until heated through, 2-3 minutes per side. Brush both sides with some of the brown sugar sauce and cook for another 1-2 minutes per side.
Transfer the ribs to a platter or plates and sprinkle with the scallions and sesame seeds. Serve hot, with the remaining brown sugar sauce on the side.