Heat the oven to 425°F with a rack in the middle. Line a large rimmed sheet pan with parchment paper or foil for easier cleanup.

Put the sweet potatoes and red onion on the sheet pan.

Drizzle the vegetables with 1 1/2 tablespoons of the olive oil. Sprinkle them with 1 teaspoon of the kosher salt and 1/2 teaspoon of the smoked paprika.

Toss the sweet potatoes and onion right on the pan until they are coated. Spread them into a single layer so they roast instead of steam.

Roast the vegetables for 15 minutes, until the onion starts to soften and the sweet potatoes begin to color on the edges.

While the vegetables roast, put the chicken thighs in a medium bowl.

Add 1 1/2 tablespoons of the olive oil, the minced garlic, the remaining 1 teaspoon smoked paprika, the remaining 1 teaspoon kosher salt, and the black pepper to the bowl with the chicken. Toss until the chicken is evenly coated.

Stir 2 tablespoons of the barbecue sauce into the bowl with the chicken so the pieces have a light coating.

Put the broccoli in a second bowl. Drizzle it with the remaining 1 tablespoon olive oil and toss to coat.

Take the sheet pan out of the oven. Turn the sweet potatoes and onion with a spatula, then push them toward the outer edges of the pan to make space in the center.

Place the chicken thighs on the center of the sheet pan in a single layer. Return the pan to the oven and roast for 12 minutes.

Take the sheet pan out again. Scatter the broccoli into the open spaces around the chicken and vegetables.