Turn broiler on high with rack 2-3 inches from heat source. ( If its summer time use a grill instead, the dish is much better).
In a medium Sauce pan bring 2 cups of water to a boil. Once boiling stir in 1 cup of rice, reduce heat to low and cover. Once most of the water has been absorbed into the rice, fluff the rice with a fork and set aside.
In a large skillet add 1 Tbsp of olive oil on medium heat. Add the yellow onion to the pan and saute until the onion starts to sweat; add the shitake mushrooms. When the onions are translucent and the mushrooms skin is a slightly dark brown they are done. When the vegetables are ready add the rice to the skillet and mix them together; set aside.
In a medium skillet add 1 Tbsp of olive oil on medium heat, crack 2 eggs directly into the pan while trying to keep them separate from each other. Cook the eggs for ~3 minutes each side or until the albumin(clear part of the egg) is all white.
While everything else is cooking place your steak in a broiler safe pan, season with salt and pepper, and place it in the oven. Cook the steak for ~4 minutes each side, this should cook the steak to medium (NOTE: broilers are different in every oven and can vary cook time drastically, so cook the steak in accordance with how hot your broiler usually runs.) Once the steak is done let it rest covered in tin foil on the counter for ~5 minutes to let the juices redistribute throughout. thinly Slice the steak on a bias against the grain.
Once everything is complete, spoon rice onto your plate, followed by the steak on top and an egg on top of that. What makes this dish for me is the ketchup, so squirt it all over. ENJOY ^_^!