Cut green onion diagonally into 1-inch lengths or slice dry onion. In wok, heat oil on high heat and stir-fry onion for a few minutes. Add the beef and continue to stir-fry for another minute or so until meat is no longer red. Add sauce, stir-fry for another minute. Add ginger and remove from heat. Serve 1 1/2 to 2 cups rice into each of 4 donburi bowls. Place meat-onion on the hot rice along with 2 to 3 tablespoons sauce. Cover and serve immediately.