Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper for easy cleanup.
Dice the sweet potato into 1/2-inch cubes, slice the carrots into thin coins, and finely mince the garlic clove.
In a large mixing bowl, toss the sweet potatoes and carrots with half of the olive oil, half of the rosemary, thyme, salt, and pepper.
Spread the seasoned vegetables on one side of the prepared baking sheet and roast for 10 minutes.
While the vegetables begin to soften, rub the chicken breast with the remaining olive oil, garlic, and the rest of the herbs, salt, and pepper.
Remove the baking sheet from the oven, move the roasted vegetables to one side, and add the chicken breast and broccoli florets to the empty space.
Return the pan to the oven and roast for an additional 15-20 minutes until the chicken reaches an internal temperature of 165°F and the vegetables are golden brown.
Allow the chicken to rest for 5 minutes before slicing to keep it juicy, then serve immediately alongside the roasted vegetables.