Combine all the ingredients in a bowl and mix gently. Form into patties and place in a skillet on medium heat. Allow the patties to cook and brown on both sides, flipping them as needed. If using store bought ground beef you need to cook them well done. If you grind your own beef, cook how you like them. Set aside under foil while you finish the rest.
For the gravy:
In the same skillet, add a little oil and the mushrooms and onions over high heat. Season with salt. Cook until browned. Whisk the gravy ingredients together in a bowl and whisk them into the pan. Once the gravy thickens, remove from the heat while you fry the eggs.
To serve:
Place some rice on a plate, top with the burger, spoon over some gravy and place the egg on top. Sprinkle scallions over and serve.