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Rinse the rice under cold water. Prepare the rice according to package directions, adding the garlic powder to the water you’re using to prepare the rice. While it’s cooking (brown rice takes longer to cook than white rice), you can prepare the rest of the recipe.
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For the soft boiled eggs, bring a medium-sized pot of water to a rolling boil. Use a spoon to gently add each whole egg to the pot. Cook for 6 minutes and 30 seconds, and prepare a bowl of ice water while you wait. Use a spoon to remove the eggs from the hot water and immediately place them in the ice bath. Let them cool for 4 minutes before peeling and setting them aside.
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Heat the olive oil in a large frying pan over medium-high heat. Add the onions and cook until transparent, about 5 minutes, stirring every minute or two. Add the garlic and cook until fragrant, about 2-3 more minutes, stirring to incorporate.
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Add the mushrooms to the pan, toss together, and cover the pan. Allow the ingredients to cook, covered, for 5 minutes. This will steam the mushrooms and help them release their moisture quickly.
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Remove the lid, and continue cooking until the mushrooms deepen in color and some brown bits develop on the bottom of the pan, about 10 minutes more, stirring every few minutes or so. Add ½ of the teriyaki sauce and stir to combine. Remove from heat.
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To serve, evenly distribute the rice between 4 bowls, then evenly distribute the mushroom mixture on top of the rice. Repeat with each of the soft boiled eggs, cutting them in half first if you’d like. And repeat with the green onions, cilantro leaves, sesame seeds, and nori. Drizzle the remaining teriyaki sauce over the bowls and serve.