Step 1Combine the soy sauce, sake, mirin and sugar in a small saucepan. Cook over medium heat until the sauce is thick and syrupy, about 25 minutes. Pour into a small bowl and set it aside to cool.
Step 2Thinly slice the steak lengthwise into 2 to 3 slices, one-eighth-inch to one-fourth-inch thick. Place a steak slice flat on a cutting board or other work surface and pound to flatten. Arrange two green onions, trimmed to fit the steak, along the bottom edge. Roll the steak tightly around the green onions, until the steak is a cylinder. Tie each end of the cylinder with kitchen string to keep it from unrolling. Repeat this process with the remaining steak and onions.
Step 3Heat the sesame oil in a skillet over medium heat. Add the beef rolls and cook until they are brown on all sides, about 5 minutes. Pour the sauce over the rolls and bring to a boil. Reduce heat; simmer 5 minutes.
Step 4Remove the rolls from the skillet, cut off the string and slice the rolls into 1-inch pieces. Spoon the sauce over the sliced rolls, and serve.