Preheat your oven to 425°F (220°C). Line a large sheet pan with parchment paper for easy cleanup.
Pat the chicken dry with paper towels.
This helps the rub stick and encourages browning.
In a small bowl, mix the spice blend: smoked paprika, garlic powder, onion powder, chili powder, cumin, 1 teaspoon salt, and 1/2 teaspoon black pepper.
Place the chicken on one side of the sheet pan. Drizzle with 1 tablespoon olive oil and sprinkle about two-thirds of the spice mix over the chicken. Rub it in on both sides.
In a large bowl, toss the cauliflower florets (and optional onions/peppers) with the remaining 2 tablespoons olive oil and the rest of the spice mix.
Season with a pinch more salt. Spread on the other side of the pan in an even layer.
Roast for 15 minutes. This jump-starts the browning before adding the BBQ sauce.
Remove the pan, brush the chicken generously with half of the BBQ sauce, and toss the cauliflower lightly to promote even roasting.
Return to the oven and roast for another 10 minutes.
Brush the chicken with the remaining BBQ sauce. If you like more caramelization, switch the oven to broil for 2–3 minutes, watching closely. The sauce should bubble and lightly char at the edges.
Check doneness: Chicken is done when it reaches an internal temperature of 165°F (74°C) and juices run clear.
Cauliflower should be tender with crisp, browned edges.
Rest the chicken for 5 minutes. Garnish with chopped parsley or cilantro. Serve with lime wedges for a fresh pop of acidity.