Combine the soy sauce, sugar, sesame oil and corn oil in a large mixing bowl. Add garlic and green onion and stir together. Put short ribs into large sealable freezer bag (you may need two). Pour marinade into bag and turn bag over several times to ensure all meat pieces are covered. Refrigerate for at least four hours, but preferably overnight. Turn bag at least once in the middle of the marinating process.
Heat grill to medium-high heat before adding the meat. Drain excess marinade off short ribs and grill them until medium, about 6-8 minutes. Sprinkle with toasted sesame seeds and chopped green onions. Serves 6.
* NOTE ON RIBS: Korean-style short ribs can be found at most Asian markets. The cut is called "flanken," a strange word that refers to a strip of beef cut across the bone from the chuck end of the short ribs. Most short rib recipes call for individual bones cut into thick pieces. Kalbi is unusual in that it calls for 3 ribs, cut lengthwise across the bones, so that you end up with a strip of meat about 8-10 inches long that has 3, 1/2-inch rib bones lining the top.
You can also use the marinade for a traditional cut of short ribs, but this is best cooked by braising -– a crock pot is excellent for this type of dish. (My mother calls this version Mushy Kalbi because the meat falls off the bone and melts in your mouth.) You can also use the marinade on chicken.