Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper for easy cleanup.
Wash the sweet potato thoroughly and slice it into even, long wedges; chop the broccoli into bite-sized florets.
Place the chicken breast, sweet potato wedges, and broccoli florets onto the prepared baking sheet in a single layer.
Drizzle the olive oil over the chicken and vegetables, then sprinkle evenly with sea salt, black pepper, garlic powder, dried oregano, and smoked paprika.
Use your hands or tongs to toss the vegetables and coat the chicken thoroughly in the oil and spice mixture.
Roast in the center of the oven for 20 to 25 minutes, or until the chicken reaches an internal temperature of 165°F and the potato wedges are golden and tender.
Remove from the oven and let the chicken rest for 5 minutes before slicing it into strips and serving alongside the crispy wedges and broccoli.