Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Peel and dice the sweet potato into 1/2-inch cubes and slice the carrots into rounds.
In a large bowl, whisk together the olive oil, minced garlic, rosemary, thyme, salt, and pepper.
Add the chicken breast, diced sweet potatoes, carrots, and broccoli florets to the bowl, tossing thoroughly to coat everything in the herb oil.
Spread the chicken and vegetables in a single layer on the prepared baking sheet, ensuring they aren't overcrowded to allow for even browning.
Roast in the oven for 20-25 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender.
Let the chicken rest for 5 minutes before slicing to keep it juicy, then serve with the roasted vegetables.