Preheat your oven to 400°F (200°C) and line a large sheet pan with parchment paper for easy cleanup.
Prepare the vegetables by peeling and dicing the sweet potato into 1/2-inch cubes and slicing the carrots into 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 sweet potatoes, and sliced carrots on the prepared sheet pan.
Drizzle approximately three-quarters of the garlic-herb oil over the chicken and vegetables, tossing them well to ensure an even coating.
Roast in the center of the oven for 15 minutes.
Remove the pan briefly to add the broccoli florets, drizzling them with the remaining herb oil and tossing slightly.
Return the pan to the oven and roast for another 10-12 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender.
Allow the chicken to rest for 5 minutes before slicing it against the grain to maintain juiciness, then serve alongside the roasted vegetables.