Preheat your oven to 400°F and line a large rimmed baking sheet with parchment paper for easy cleanup.
Peel and dice the sweet potato and carrots into half-inch cubes, then cut the broccoli into small, bite-sized florets.
In a mixing bowl, toss the prepared vegetables with 0.75 tablespoon of olive oil, half of the minced garlic, and half of the salt and pepper.
Spread the seasoned vegetables in a single layer on one side of the baking sheet, leaving enough room for the chicken.
Pat the chicken breast dry and rub it thoroughly with the remaining 0.5 tablespoon of olive oil, remaining garlic, rosemary, thyme, salt, and pepper.
Place the chicken on the other side of the baking sheet and roast for 20 to 25 minutes 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 ensure it stays juicy, then serve alongside the roasted vegetables.