Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper.
Finely mince the garlic cloves and strip the leaves from the rosemary and thyme sprigs, chopping them finely.
In a small bowl, whisk together the olive oil, minced garlic, chopped rosemary, thyme, sea salt, and black pepper.
Place the chicken breast, broccoli florets, and sliced carrots on the prepared baking sheet.
Drizzle the garlic-herb oil mixture over the chicken and vegetables, using your hands or a brush to ensure the chicken is well-coated and tossing the vegetables to distribute the oil.
Spread the ingredients out into a single layer so they roast evenly rather than steaming.
Roast in the center of the oven 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 allow the juices to redistribute.