Preheat oven to 400 degrees. Set racks in the upper and lower thirds of the oven. In a large bowl, pat the chicken dry with paper towels. Add 1 tablespoon oil and toss to coat. Season chicken with 1 teaspoon salt, 1/2 teaspoon pepper, and coriander. Rub in the seasoning and set aside at room temperature.
In a large bowl, whisk together 2 tablespoons oil, miso paste, vinegar, soy sauce, honey, and 1/2 teaspoon each salt and pepper. Add vegetables and garlic cloves to the bowl and toss to coat. Transfer to a rimmed baking sheet, place on the upper rack of the oven, and roast until softened and browned, 40 to 45 minutes, tossing a few times during roasting. Peel garlic and discard skins.
Meanwhile, heat a large skillet over medium-high heat with 1 tablespoon oil. Once hot, add half the chicken thighs skin side down. Cook until skin is golden brown, 6 to 8 minutes. Remove from skillet and place skin side up on a second rimmed baking sheet. Repeat with remaining chicken thighs, reserving skillet with fat after cooking. Transfer baking sheet to lower rack of oven and roast until the chicken's internal temperature reaches 165 degrees, 12 to 15 minutes more.
Discard stems from reserved beet and turnip greens; wash and roughly chop the leaves. Pour out all but 2 teaspoons of oil from the skillet and place the pan over medium-high heat. Add the greens to the pan with 2 tablespoons water and 1/4 teaspoon salt and cook, tossing, until wilted, 1 to 2 minutes. Transfer roasted vegetables to a serving bowl, add the sautéed greens, and toss to combine. Taste and adjust seasoning. Serve chicken thighs with vegetables and lime wedges. (Recipe #315)