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Step 1
Place 2 tablespoons unsalted butter in a small bowl and let sit at room temperature until softened.
Step 2
Arrange a rack in the middle of the oven and heat the oven to 375˚F. Meanwhile, halve and thinly slice 1 medium yellow onion. Cut 1 1/2 pounds green cabbage through the core into wedges about 2-inches wide. Cut out the core, then cut the remaining cabbage into 1/2-inch thick slices (about 8 cups). Thinly slice 4 large garlic cloves.
Step 3
Add 1/4 cup white miso paste, 1 tablespoon honey, 3/4 teaspoon kosher salt, and 1 teaspoon black pepper to the bowl of butter and smash and mix until combined.
Step 4
Pat 4 bone-in, skin-on chicken thighs dry with paper towels. Spread 1/4 cup of the miso mixture all over the chicken thighs.
Step 5
Heat 1 tablespoon plus 1 1/2 teaspoons olive oil in a large Dutch oven over medium heat until shimmering. Add the chicken skin side-down and cook undisturbed until the skin is deeply browned and caramelized, about 4 minutes. Flip the chicken and continue to cook until the second side is golden brown, about 2 minutes more. Using tongs, transfer the chicken to a plate skin-side up (they will not be cooked through at this point).
Step 6
Add the onion to the fat in the pot and cook, stirring occasionally, until deeply fragrant and lightly browned, about 1 minute. Add the cabbage and cook, stirring often, until the cabbage is golden brown in spots and wilted by half, about 7 minutes. Add the garlic and remaining miso mixture and cook, stirring occasionally, until the garlic is fragrant and the butter is melted, about 1 minute.
Step 7
Add 1/2 cup dry white wine and 1/3 cup low-sodium soy sauce. Cook, scraping up any browned bits from the bottom of the pot, until the smell of alcohol burns off, about 2 minutes. Turn off the heat.
Step 8
Return the chicken to the pot skin-side up, placing them on top of the cabbage; pour in any accumulated juices on the plate. Transfer the pot to the oven and bake until the chicken is cooked through and the cabbage is wilted by half, about 30 minutes. Meanwhile, finely chop fresh cilantro leaves or fresh chives for garnish. Sprinkle over the chicken and cabbage before serving.