Adjust oven rack to lower-middle position and preheat oven to 325ºF. Heat oil in oven-safe Dutch oven over high heat until shimmering. Season meat generously with pepper, then sear until browned on all sides, about 4 minutes per side. Remove short ribs.
Reduce heat to medium. Add garlic and ginger stirring constantly, until browned about 2 minutes. Add mirin and scrape up any browned bits from bottom of Dutch oven.
Add 1 cup water, ponzu sauce, soy sauce, apple juice, rice vinegar, sesame oil and brown sugar; stir to combine. Return short ribs to pan. Bring to a simmer, cover and transfer to oven. Braise, turning beef once and adding water if necessary to keep it halfway submerged throughout cooking, until beef is fork tender, about 2 1/2 to 3 hours.
Transfer beef to a platter and skim fat from cooking juices in Dutch oven. Taste cooking juices, if too concentrated, dilute to taste with additional water and/or mirin.
Combine corn starch with remaining 1/4 cup water in a small bowl, whisking thoroughly to remove any lumps. Whisk cornstarch slurry into cooking juices, bring to a boil over high heat, and cook until gravy is thickened, about 2 minutes. Add 1 tablespoon toasted sesame seeds to sauce.
Bring water, milk and salt to a boil in a heavy 2-quart saucepan. Slowly add the grits in a thin, steady stream stirring constantly with a wooden spoon.
Reduce the heat to low and simmer, stirring occasionally until the grits thicken, 10 to 15 minutes. Off the heat whisk in the butter, pepper, wasabi and soy sauce.
Serve short ribs with sauce over wasabi-soy grits, with pickled ginger and green onion garnish. Finish with a sprinkle of toasted sesame seeds.