Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper for easy cleanup.
Slice the half sweet potato into 1/2-inch thick rounds and toss them with a tiny drizzle of olive oil and a pinch of salt, then place them on one side of the baking sheet.
Pat the chicken thighs completely dry with paper towels to ensure a good sear in the oven.
In a small bowl, combine the smoked paprika, garlic powder, onion powder, sea salt, and black pepper.
Rub the chicken thighs with the remaining olive oil and then coat thoroughly with the spice blend.
Place the chicken on the baking sheet next to the sweet potatoes and roast for 15 minutes.
Remove the sheet from the oven, add the broccoli florets to the open space, and brush the top of the chicken thighs with the sugar-free BBQ sauce.
Return the pan to the oven and roast for an additional 10 to 12 minutes until the chicken reaches an internal temperature of 165°F and the vegetables are tender.
Let the chicken rest for 5 minutes before serving to allow the juices to redistribute.