Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper.
Peel and cube the sweet potato into 1/2-inch pieces, then place them on the baking sheet with the broccoli florets.
Drizzle the vegetables with 0.5 tbsp of olive oil and sprinkle with half of the salt and pepper; toss to coat evenly.
Roast the vegetables for 20-25 minutes, tossing halfway through, until the potatoes are tender and the broccoli is slightly charred.
While the vegetables roast, season the chicken breast on both sides with smoked paprika, garlic powder, and the remaining salt and pepper.
Heat the remaining 0.5 tbsp of olive oil in a medium skillet over medium-high heat.
Place the chicken in the skillet and sear for 6-7 minutes per side, or until the exterior is golden brown and the internal temperature reaches 165°F.
Remove the chicken from the pan and let it rest for 5 minutes before slicing and serving alongside the roasted vegetables.