Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Peel and cube the sweet potato into 1/2-inch pieces and slice the carrots into rounds.
In a bowl, toss the sweet potatoes and carrots with half of the olive oil and a pinch of the salt and pepper.
Spread the root vegetables onto the baking sheet and roast for 10 minutes.
While the vegetables are roasting, mince the garlic and combine it in a small bowl with the remaining olive oil, rosemary, thyme, salt, and pepper.
Rub the garlic-herb mixture evenly over the chicken breast.
Remove the baking sheet from the oven, move the root vegetables to one side, and add the chicken breast and broccoli florets to the other side.
Drizzle any remaining herb oil over the broccoli and return the pan to the oven.
Roast for an additional 15-20 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are golden and tender.
Remove from the oven and let the chicken rest for 5 minutes before slicing to ensure it stays juicy.