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1
Bring mushrooms, sugar, 1/2 cup soy sauce, 1/2 cup vinegar, and 1 cup water to a simmer in a small saucepan over medium-high heat and cook, stirring occasionally, until sugar is dissolved, about 5 minutes. Transfer mushrooms to a medium bowl with a slotted spoon. Let brine cool, then pour over mushrooms. Cover and chill at least 1 hour.
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2
Meanwhile, rinse rice until water runs clear (this removes surface starch and keeps rice from getting gummy). Combine rice and 2 cups water in a medium saucepan, season with salt, and let sit 30 minutes.
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3
Bring rice to a boil. Reduce heat to low, cover, and cook until tender, 30-35 minutes (you can also use a rice cooker). Remove from heat and let sit, covered, 15 minutes; fluff with a fork. Keep warm.
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4
Soak wakame in 1/2 cup cold water in a small bowl until softened, 6-8 minutes. Drain and mix in a clean small bowl with black bean paste, honey, oil, remaining 5 tsp. soy sauce, and remaining 5 tsp. vinegar. Add tofu to spicy black bean shoyu, season with salt, and gently toss. Let sit 10 minutes to let flavors meld. Taste and season with more salt if needed.
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5
Divide rice among bowls and spoon tofu mixture on top of rice. Arrange drained pickled shiitake mushrooms, scallions, peanuts, and some tobiko, if using, around tofu mixture.
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6
Mushrooms can be pickled 5 days ahead. Keep chilled.
