Sprinkle brown sugar over beef and mix well to evenly coat. Let sit at room temperature for 10 minutes while preparing marinade. In a bowl, whisk together remaining ingredients. Transfer beef into a large sealable freezer bag (you may need 2). Add marinade, press out excess air from bags, and seal. Turn bag over several times to ensure beef is evenly coated. Refrigerate for at least 4 hours but preferably overnight.
Heat gas or charcoal grill to medium-hot. Drain excess marinade off beef. Grill short ribs, turning once, to desired doneness, about 3 to 4 minutes per side. Garnish with thinly sliced green onions, if desired. Serve whole pieces as a main course or cut into smaller pieces, using kitchen shears, for a starter or party nibble.
* NOTE: Korean-style short ribs can be found at most Asian markets. The cut, also known as "flanken," refers to a strip of beef cut across the bone from the chuck end of the short ribs. Unlike American and European-style short ribs, which include a thick slice of bone-in beef, Korean-style short ribs are cut lengthwise across the rib bones. The result is a thin strip of meat, about 8 to10 inches in length, lined on 1 side with 1/2-inch thick rib bones. The thin slices make for fast cooking on the grill.
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