Preheat and prep the pan: Heat the oven to 425°F (220°C). Line a large rimmed sheet pan with parchment for easier cleanup.
Season the chicken: In a bowl, toss chicken pieces with 1/2 cup BBQ sauce, smoked paprika, garlic powder, chili powder, a pinch of salt, and pepper.
Coat well and set aside.
Coat the gnocchi and veggies: On the sheet pan, add gnocchi, onion, bell pepper, and broccoli. Drizzle with olive oil, sprinkle with a little salt and pepper, and toss directly on the pan to coat.
Add the chicken: Scatter the seasoned chicken over the gnocchi and vegetables. Spread everything out in a single layer so it roasts, not steams.
Roast: Bake for 15 minutes.
Stir and flip the gnocchi and chicken so they brown evenly.
Glaze with sauce: Brush or drizzle another 1/2 cup BBQ sauce over the chicken and gnocchi. Return to the oven and roast for 8–10 minutes more, until the chicken is cooked through (165°F) and the gnocchi are golden at the edges.
Finish and serve: Toss everything gently with the remaining 1/2 cup BBQ sauce to taste. Garnish with parsley or green onions.
Serve hot with lime wedges or a light ranch drizzle if you like.