Heat 2 tablespoons oil in a large skillet over medium high heat, and cook the sliced onions for about 10 minutes, stirring often.
Add the beef and sugar, and cook until the beef is slightly browned. Add the mirin, soy sauce, and stock. Bring to a simmer, and cook for about 10-15 minutes to reduce the stock into a thin sauce. Taste for seasoning, and add a little more soy sauce if needed.
Meanwhile, heat another couple tablespoons of oil in a cast iron or non-stick skillet. Cook the eggs sunny-side up. You can cook them in batches if needed. The yolks should still be runny!
When the beef is done simmering, divide the rice among 4 bowls, and top with the beef and an egg for each bowl. Garnish with chopped scallion and toasted sesame seeds, if using.