Preheat your oven to 425°F (220°C). Line a large baking sheet with parchment paper for easier cleanup, if desired.
In a large mixing bowl, combine the broccoli florets, sliced bell peppers, red onion wedges, and cherry tomatoes. Drizzle with 2 tablespoons of olive oil, season with salt and pepper, and toss until well-coated. Spread the vegetables evenly on one side of the baking sheet.
In the same mixing bowl, add the chicken thighs. Drizzle with the remaining tablespoon of olive oil, and add the garlic powder, onion powder, smoked paprika, salt, black pepper, and BBQ sauce. Toss until the chicken is evenly coated in the spices and sauce.
Place the chicken thighs on the other side of the baking sheet, ensuring they are not overcrowded.
Roast in the preheated oven for about 30 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and the vegetables are tender and slightly caramelized.
Remove the sheet pan from the oven. Let the chicken rest for a few minutes, then garnish with freshly chopped parsley if desired.
Serve hot and enjoy your flavorful BBQ sheet-pan chicken with the roasted vegetables.