Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Peel and dice the sweet potato into 1-inch cubes and slice the carrots into rounds.
Place the sweet potatoes and carrots on the baking sheet, drizzle with half of the olive oil, and season with half of the salt and pepper.
Roast the vegetables for 10 minutes to give them a head start.
While the vegetables roast, mince the garlic and finely chop the fresh rosemary.
Rub the chicken breast with the remaining olive oil, minced garlic, rosemary, and the rest of the salt and pepper.
Remove the baking sheet from the oven, move the potatoes and carrots to one side, and add the chicken breast and broccoli florets to the other side.
Return the pan to the oven and roast for an additional 18 to 22 minutes, or until the chicken reaches an internal temperature of 165°F.
Remove from the oven and let the chicken rest for 5 minutes before slicing to keep it juicy.