Preheat and prep. Heat the oven to 425°F (220°C). Line a large sheet pan with parchment or foil for easy cleanup. Pat the chicken dry with paper towels.
Season the chicken. In a small bowl, mix 1 teaspoon salt, 1/2 teaspoon black pepper, 1 teaspoon smoked paprika, and 1/2 teaspoon onion powder.
Rub evenly over the chicken.
Mix the veggies. Toss the peppers, onion, zucchini, broccoli, and carrots with 3 tablespoons olive oil, 2 minced garlic cloves, 1 teaspoon smoked paprika, 1/2 teaspoon salt, and a few grinds of pepper. Spread in a single layer on the sheet pan.
Add the chicken. Nestle the seasoned chicken pieces among the vegetables. Make sure nothing is piled too high so everything roasts, not steams.
Roast first round. Bake for 15 minutes.
Meanwhile, stir together BBQ sauce with 1 tablespoon apple cider vinegar and 1 teaspoon honey for a glossy finish.
Glaze the chicken. Remove the pan, brush a generous layer of BBQ sauce over the chicken, and flip the veggies for even browning. If using cherry tomatoes, add them now.
Roast second round. Return to the oven for 10–12 minutes, until the chicken reaches an internal temperature of 165°F (74°C) and the veggies are tender with charred edges.
Optional broil. For extra char, switch to broil for 1–2 minutes. Keep a close eye—sugary sauces can burn quickly.
Rest and finish. Let the chicken rest 5 minutes.
Brush with a little more BBQ sauce if you like. Squeeze lemon over the veggies and sprinkle with fresh herbs.
Serve. Plate the chicken with a big scoop of roasted veggies. Add extra BBQ sauce on the side.