Pat the steak dry with paper towels, then season both sides with salt and black pepper.
Cook the steak on an outdoor grill or indoors in a hot skillet or grill pan until medium rare, or until it reaches your preferred doneness.
Transfer the steak to a cutting board and let it rest for at least 5 minutes before slicing it against the grain.
Meanwhile, add the soy sauce, mirin, sake, and sugar to a small saucepan. Bring to a gentle simmer and cook for 2–3 minutes, stirring until the sugar has completely dissolved. Remove from the heat.
Divide the warm cooked rice between two bowls, shaping each portion into a dome.
Arrange the sliced steak over the rice and spoon the donburi sauce over the top.
Place an egg yolk in the center of each bowl, if using, and garnish with sliced scallion greens. Serve immediately.