Preheat your oven to 400°F (200°C).
Peel the sweet potato and cut it into 1/2-inch cubes.
On a parchment-lined baking sheet, toss the sweet potato cubes with half of the olive oil, sea salt, and smoked paprika.
Roast the sweet potatoes for 20-25 minutes, tossing halfway through, until they are golden and caramelized on the edges.
While the potatoes roast, season the chicken breast with garlic powder and black pepper.
Heat the remaining olive oil in an oven-safe skillet over medium-high heat and sear the chicken for 3-4 minutes per side until browned.
Brush the chicken generously with the BBQ sauce and transfer the skillet to the oven for the last 8 minutes of the potato roasting time.
Steam the broccoli florets in a steamer basket for 4-5 minutes until they are tender-crisp and bright green.
Remove the chicken and potatoes from the oven, let the chicken rest for 3 minutes, then plate everything together.