In a heavy, nonstick skillet, heat the butter to medium high heat. Add the steak and cook until well browned. Remove from pan and set aside. Add the green onions and garlic and cook for about a minute. Add the broccoli and cook for about 3 minutes. Move the broccoli to one side and add the eggs to the other. Cook the eggs to your liking and remove from the pan.

Add the steak back to the pan with the broccoli and stir until heated through. Serve the steak and broccoli topped with an egg.