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Step 1
Adjust oven rack to lower-middle position and preheat oven to 325°F. Heat oil in an 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.
Step 2
Reduce heat to medium. Add garlic and ginger and cook, stirring constantly, until browned, about 2 minutes. Add mirin and scrape up any browned bits from bottom of Dutch oven. Add ponzu sauce, soy sauce, apple juice, sesame oil, 1/2 cup water, brown sugar, and vinegar and stir to combine.
Step 3
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 3 1/2 hours.
Step 4
Transfer beef to a platter and skim fat from cooking juices in Dutch oven. Taste cooking juices: If too concentrated, dilute to taste with water and/or mirin. Combine cornstarch with remaining 2 tablespoons water, 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.
Step 5
Serve short ribs over rice, drizzled with gravy and garnished with green onion and pear.