Preheat your oven to 400°F and line a large sheet pan with parchment paper for easy cleanup.
Mince the garlic cloves and dice the potato into 1/2-inch cubes, then slice the carrots into thin rounds.
In a small bowl, whisk together the olive oil, minced garlic, dried rosemary, dried thyme, sea salt, and black pepper.
Place the chicken breast, diced potatoes, and sliced carrots on the prepared sheet pan.
Drizzle approximately three-quarters of the herb oil mixture over the chicken and vegetables, tossing well to ensure everything is evenly coated.
Roast in the oven for 15 minutes.
Remove the pan from the oven, add the broccoli florets to the tray, and drizzle them with the remaining herb oil.
Return the pan to the oven and roast for an additional 10 to 12 minutes, or until the chicken reaches an internal temperature of 165°F and the potatoes are golden and tender.
Allow the chicken to rest for 5 minutes before slicing to keep it juicy, then serve alongside the roasted vegetables.