Prepare the Oven and Marinade: Adjust the oven rack to the upper-middle position and preheat to 475°F. In a large bowl, whisk together olive oil, sage, honey, salt, and pepper. In a separate bowl, combine yogurt, water, minced garlic, orange zest, and 1 tablespoon of the oil mixture; set the yogurt sauce aside for serving.
Add kale to a large bowl and massage with your hands until the leaves are softened and slightly wilted, about 1 minute. Toss in the butternut squash, shallots, dried cranberries, whole garlic cloves, and ¼ cup of the oil mixture. Stir to combine.
Whisk the paprika into the remaining oil mixture. Add the chicken and toss to coat evenly.
Spread the vegetable mixture in a single layer on a rimmed baking sheet. Place the chicken, skin side up, on top of the vegetables. Roast for 25–35 minutes, or until the chicken registers 160°F, rotating the sheet halfway through roasting.
Transfer the chicken to a serving platter, tent with aluminum foil, and let rest for 5 minutes. Toss the roasted vegetables with pan juices, season with additional salt and pepper to taste, and transfer to the platter with the chicken. Drizzle ¼ cup of the reserved yogurt sauce over the chicken, serving the remainder on the side.