Spread sweet potatoes and broccoli on a large sheet pan. Drizzle with olive oil, sprinkle with chili powder and season to taste with salt and pepper. Toss to combine.
Season chicken with salt and pepper to taste, then spread the thighs on the sheet pan, pushing the vegetable aside to create space for the chicken. In a small bowl, whisk together barbecue sauce, honey and garlic. Pour a generous amount onto each chicken thigh.
Bake until the chicken is cooked through and the vegetables are tender, about 30-40 minutes.
