Preheat your oven to 400°F (200°C) and line a large sheet pan with parchment paper.
Wash and scrub the sweet potato, then cut it into even wedges.
Place the sweet potato wedges on the pan, drizzle with half of the olive oil, and sprinkle with half of the salt and pepper.
Roast the sweet potatoes for 10 minutes to give them a head start.
While the potatoes roast, mince the garlic and combine it in a small bowl with the remaining olive oil, rosemary, and thyme.
Pat the chicken breast dry and rub it thoroughly with the garlic-herb oil mixture.
Remove the pan from the oven, move the potatoes to one side, and place the chicken breast and broccoli florets on the other side.
Season the broccoli and chicken with the remaining salt and pepper.
Return the pan to the oven and roast for 15 to 20 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender.
Let the chicken rest for 5 minutes before slicing and serving alongside the roasted vegetables.