1. Preheat your oven to 400°F (200°C) and line a large sheet pan with parchment paper for easy cleanup.
2. Cut the chicken breast into bite-sized pieces and slice the carrots, zucchini, and broccoli into uniform shapes to ensure even cooking.
3. In a large mixing bowl, combine the chicken, vegetables, minced garlic, olive oil, dried thyme, dried rosemary, sea salt, and black pepper.
4. Toss everything thoroughly until the chicken and vegetables are well-coated with the oil and herb mixture.
5. Spread the mixture in a single layer on the prepared sheet pan, ensuring nothing is overcrowded so the vegetables roast rather than steam.
6. Roast in the center of the oven for 20 to 25 minutes, or until the chicken is cooked through and the vegetables are tender and lightly browned.
7. Remove from the oven and let rest for a few minutes before serving to allow the juices to redistribute.