Heat the oven: Preheat to 425°F (220°C). Line a large sheet pan with parchment for easier cleanup.
Prep the veggies: In a large bowl, toss potatoes, onion, peppers, and broccoli with olive oil, smoked paprika, garlic powder, onion powder, salt, and pepper.
Start the potatoes first: Spread potatoes and onions on the sheet pan and roast for 10 minutes.
This gives them a head start so everything finishes together.
Season the chicken: Pat chicken dry, season both sides with salt and pepper, and brush with about half the BBQ sauce.
Add everything to the pan: Remove the pan from the oven. Add the peppers and broccoli, then nestle the chicken among the veggies.
Roast: Return to the oven and cook for 15 minutes.
Glaze and finish: Brush the chicken with more BBQ sauce and toss a little sauce over the veggies if you like. Roast 5–10 more minutes, until the chicken reaches 165°F (74°C) and the veggies are tender with crisp edges.
Broil for char (optional): Broil 1–2 minutes to caramelize the sauce.
Watch closely to prevent burning.
Rest and serve: Let the chicken rest 5 minutes. Garnish with parsley or green onions and serve with lemon wedges for brightness.