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1
Cut daikon into twelve 1/2-inch slices. Combine sake, mirin, soy, 2 tablespoons sugar, 1/2 cup water, and konbu (if using) in a medium saucepan. Add daikon slices and shiitake. Bring to a boil over high heat. Reduce to a bare simmer. Cover and cook, turning and rotating daikon occasinally until daikon is completely tender and colored all the way through, about 30 minutes. Transfer daikon and mushrooms to a paper towel-lined plate to drain. Return remaining liquid to a gently boil over medium heat and cook until reduced to 1/4 cup, about 10 minutes. Set aside.
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2
While daikon is cooking, place mung bean sprouts in a medium bowl. Combine vinegar, remaining 1/2 cup water, remaining 1/2 cup sugar, 1 teaspoon kosher salt, and jalapeno in a medium saucepan. Bring to a boil over high heat, stirring to dissolve sugar. Pour hot liquid over bean sprouts, then place a clean, lint-free paper towel or kitchen towel directly on the surface of the liquid, pressing down until it is completely saturated and keeps the bean sprouts submerged. Set aside to cool.
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3
Combine mayonnaise and chili-garlic sauce in a blender and blend until smooth. Transfer to a bowl and set aside.
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4
When daikon and shiitake are cooked, place steamed buns on a plate and cover with a damp paper towel. Microwave on high power until hot, about 1 minute. Spread spicy mayonnaise in each steamed bun, then add a slice of simmered daikon and a shiitake, a drizzle of the reduced simmering liquid, some pickled mung bean sprouts, sliced scallions, and cilantro leaves. Close sandwiches and serve with extra miso mayonnaise on the side for dipping. Excess mung bean sprouts can be stored submerged in pickling liquid in a sealed container in the refrigerator for up to 1 month. Extra mayonnaise can be stored in a sealed container in the refrigerator for up to 2 weeks.
