Bring water to a boil in a small sauce pan.

Add a pinch of salt and the rice to the boiling water.

Stir and reduce the heat to low.

Cover and let simmer for 15 minutes.

Remove from heat and let stand, covered, for 5 minutes, then fluff with a fork.

Heat a cast iron skillet over medium-high heat.

Lightly grease the skillet with butter.

Sear the ground beef ball in the skillet for 1 minute.

Flip the beef and smash into a patty. Sprinkle patty with salt and pepper.

When liquid starts to bubble through the patty and the bottom is browned (about 3-4 minutes), flip the patty and cook for an additional 3-4 minutes until browned on the bottom.

Remove the burger from the skillet and set aside.

Reduce heat under the skillet to medium.

Depending on the amount of fat remaining in the pan, add up to 1 Tbsp. of butter and heat until it stops bubbling.

Add the sliced onions to the butter and sauté until soft (4-5 minutes).

Add the chopped white parts of the scallion and the garlic to the skillet and sauté for 1 minute.

Add the grated ginger to the skillet and mix thoroughly.

Sprinkle flour over the onions and stir thoroughly. Let the flour toast until a roux is formed.

Pour in the hot beef stock, soy sauce, Worcestershire sauce, and mirin.

Add black pepper and stir thoroughly.

Reduce the heat under the skillet to low and let the gravy simmer and reduce (5-7 minutes).

Return the burger patty to the skillet and cover with gravy.

Heat a second skillet over medium heat and melt 1 Tbsp. of butter.

Crack an egg into the skillet and sprinkle with salt and black pepper.

Reduce heat to low, add 2 tsp. of water to the skillet.

Cover and let cook for 2 minutes.

Cover the bottom of a shallow bowl with rice.

Add the burger patty to the top of the rice.

Pour gravy over the burger and rice.

Slide the fried egg on top of the gravy.

Garnish with the chopped green part of the scallion.