Blanch asparagus in boiling water for 1 to 2 minutes. Drain and shock in cold water to stop cooking. Reserve the tips (about 2 inches in length) for garnishing. Cut the stalks into tiny coins about 1/8 inch thick. Set aside.
Seasoned Mushrooms
Place mushrooms, soy sauce, mirin, and sugar in a small saucepan. Do not worry if it appears too dry initially. Mushrooms will release a lot of liquid when cooked. Simmer over low heat for 20 minutes. Remove and slice mushroom caps thinly when cool enough to handle. Set aside.
Scrambled Eggs (Tamago Soboro)
Heat a 10-inch non-stick skillet with 1 tsp vegetable oil over medium heat. Pour egg mixture into the pan and stir constantly with a pair of chopsticks or a whisk. When eggs begin to set, remove pan from heat but continue to stir until eggs are no longer wet. This should only take 2 to 3 minutes. Remove and set aside.
Putting it together and serving
Mix sushi rice, sliced asparagus, mushrooms, and sesame seeds in a large bowl. Divide into 4 individual bowls.
Scatter scrambled eggs over the rice and garnish with asparagus tips.