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Preheat the oven to 425ºF. Pour a teaspoon of neutral oil over a rimmed sheet pan. Rub to coat.
In a small bowl, stir together the sesame oil, coconut oil, soy sauce, rice vinegar, and sriracha, if using. Place chicken in a large bowl. Season all over with salt and pepper. Pour 1/4 cup of the prepared mixture over the chicken and let marinate while the oven preheats. (Chicken can marinate longer, too, but try, if time permits, to bring it to room temperature before cooking—the coconut oil will solidify in the fridge and look clumpy, which is fine.)
Cut the cabbage in half through the core. Cut again through each core and repeat this process until you are left with many wedges, no greater than 1-inch wide. Place the wedges in a large bowl, season all over with salt and pepper, and toss with the remaining dressing.
Place chicken on prepared sheet pan spreading it out evenly. Roast for 10 minutes. Remove pan from oven, and nestle cabbage wedges all around the pieces, tucking it under if necessary—it will feel like a lot of cabbage. Roast for 20 to 25 minutes more or until chicken is golden and cooked through. Remove pan from oven, transfer chicken to a platter to rest. Return cabbage to the oven to roast for 10 to 15 minutes more, or until juices have reduced and edges of cabbage wedges are caramelized.