Preheat your oven to 400°F (200°C) and line a large sheet pan with parchment paper for easy cleanup.
Peel and cube the sweet potato into 1/2-inch pieces and slice the carrots into rounds.
In a large bowl, toss the sweet potatoes, carrots, and broccoli florets with half of the olive oil, half of the salt, and half of the pepper.
Mince the garlic cloves and combine them in a small bowl with the remaining olive oil, rosemary, thyme, salt, and pepper to create a herb rub.
Pat the chicken breast dry with a paper towel and coat it thoroughly with the garlic-herb mixture.
Spread the vegetables out on the prepared sheet pan, making room in the center for the chicken breast.
Place the chicken on the pan and roast for 20 to 25 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender and slightly browned.
Remove from the oven and let the chicken rest for 5 minutes before slicing to ensure the juices stay locked in.