Place the dried mushrooms in a medium-sized bowl. Pour the boiling water over top and let sit for 30 minutes. Drain the mushrooms and reserve the steeping liquid.

Heat the olive oil over medium heat until shimmering. Add the shallots and half the salt. Saute until slightly softened. About 2-3 minutes.

Add the mushrooms to the shallots and saute until softened and slightly caramelized. Deglaze the pan with the sake and add the remaining salt.

Pour the beef stock into the skillet and bring the mixture to a boil. Reduce the heat to a simmer and let cook for 15 minutes.

Place the cornstarch in a small bowl. Spoon off a small amount of the liquid from the skillet and add it to the cornstarch. Whisk to combine.

Pour the cornstarch mixture into the skillet and cook until thick enough to coat the back of a spoon.

Remove the gravy from the heat and keep warm until ready to serve.

Cook the rice according to package directions. Once the moisture is absorb, fluff the rice with a fork and transfer to a large bowl.

Add the umeboshi, mint and ginger to the rice and toss until everything is evenly distributed.

Keep warm until ready to serve.

Form the ground beef into 2 patties. Sprinkle both sides of the patties with salt and pepper and set aside.

Heat a seasoned cast iron skillet over high heat until smoking. Add the patties and reduce the heat to medium. Cook the burgers roughly 5 minutes a side or until the internal temperature reaches between 145°F - 160°F.

Remove the burgers from the heat and tent with foil.

Heat a small amount of olive oil in a non-stick pan over medium heat. Crack the eggs into the pan and cook to your preference. I recommend sunny-side-up with a slightly runny yolk.

Spoon some rice onto two plates. Top the rice with a hamburger patty, then top the hamburger patty with a generous spoonful of Shiitake Gravy. Finish the dish with a fried egg and sprinkle with furikake if desired.