Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Peel and dice the sweet potato into 1/2-inch cubes and slice the carrots into rounds.
In a large bowl, toss the sweet potato, carrots, and broccoli florets with half of the olive oil, half of the rosemary, half of the thyme, and a pinch of salt and pepper.
Place the chicken breast on one side of the prepared baking sheet and rub with the remaining olive oil, minced garlic, rosemary, thyme, salt, and pepper.
Spread the seasoned vegetables in a single layer on the other side of the baking sheet.
Roast in the oven for 20-25 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender and slightly browned.
Let the chicken rest for 5 minutes before slicing to ensure it stays juicy, then serve alongside the roasted vegetables.