Preheat your oven to 400°F (200°C).
Peel and cube the sweet potato into 1/2-inch pieces, then slice the carrots into rounds.
On a large parchment-lined sheet pan, toss the sweet potato cubes with 0.5 tbsp of olive oil and a pinch 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 whisk it in a small bowl with the remaining 0.5 tbsp of olive oil, rosemary, thyme, and the rest of the salt and pepper.
Rub the garlic-herb oil mixture evenly over the chicken breast.
Remove the pan from the oven and add the chicken breast, broccoli florets, and sliced carrots to the sheet pan.
Return the pan to the oven and roast for 18-22 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender.
Allow the chicken to rest for 5 minutes before slicing to ensure every bite is juicy and flavorful.