Combine soy sauce, sake, mirin, brown sugar, ginger, green onions, and turmeric in a large mixing bowl and whisk until combined. Add the short ribs and toss until thoroughly and evenly coated.
Cover with plastic wrap and marinate in the refrigerator for 4 to 12 hours, tossing occasionally.
Preheat a charcoal grill for high heat.
Remove meat from the refrigerator. Grill over very hot charcoal until slightly caramelized and just cooked through, 2 to 3 minutes per side. Any excess marinade can be used to baste the meat while it's grilling. Flip meat after basting to allow to caramelize, about 1 minute more per side.
Serve immediately, spooning or brushing on any accumulated juices from the plate.