Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper.
Peel and dice the sweet potato into 1/2-inch cubes and slice the carrots into thin rounds.
In a small bowl, whisk together the olive oil, minced garlic, finely chopped rosemary, thyme, sea salt, and black pepper.
Place the chicken breast on one side of the prepared baking sheet and arrange the sweet potatoes and carrots on the other side.
Brush half of the herb oil mixture over both sides of the chicken and toss the remaining half with the sweet potatoes and carrots until well coated.
Roast in the center of the oven for 15 minutes.
Remove the pan briefly to add the broccoli florets to the vegetable side, tossing them quickly in the existing pan juices.
Return to the oven for another 10-12 minutes until the chicken reaches an internal temperature of 165°F and the vegetables are tender and lightly browned.
Let the chicken rest for 5 minutes before slicing to keep it moist and juicy.