Preheat the oven to 425 degrees F and line a rimmed baking sheet with parchment paper. Place the chicken thighs skin-side up on one side of the baking sheet, spacing them evenly apart. Roast until they turn opaque on the outside, 15 minutes.
Remove the baking sheet from the oven and place the sweet potato wedges in the center. Drizzle the potatoes with 2 tablespoons of the olive oil and sprinkle with chili powder and some salt. Use tongs to toss the potatoes so each piece is evenly coated. In the remaining open area of the pan, toss the Brussels sprouts with the remaining 2 tablespoons of olive oil and and sprinkle with salt and pepper. Arrange the Brussels sprouts cut-side down on the pan and brush each chicken thigh with barbecue sauce on all sides.
Return the baking sheet to the oven and roast until the chicken is completely cooked through and reads an internal temperature of 160 degrees F, and the Brussels sprouts and sweet potato wedges are tender and charred in spots, 25 to 30 minutes more. Toss the vegetables with the accumulated juices on the tray before serving.
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