Preheat your oven to 400°F and line a large rimmed baking sheet with parchment paper.
Peel the sweet potato and cut into 1-inch cubes, then slice the carrot into half-inch rounds.
In a medium bowl, toss the sweet potato and carrot with half of the olive oil and a pinch of sea salt.
Mince the garlic cloves and finely chop the fresh rosemary and thyme leaves.
Rub the chicken breast evenly with the remaining olive oil, minced garlic, chopped herbs, sea salt, and black pepper.
Place the chicken breast in the center of the baking sheet and surround it with the prepared sweet potatoes and carrots.
Roast for 15 minutes, then remove the pan and add the broccoli florets, tossing them quickly in the pan juices.
Return the pan to the oven and roast for an additional 10 to 12 minutes until the chicken reaches an internal temperature of 165°F.
Allow the chicken to rest for 5 minutes before slicing to ensure the meat remains tender and juicy.