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-inch cubes and thinly slice the carrots into rounds.
In a large mixing bowl, toss the sweet potato cubes, sliced carrots, and broccoli florets with half of the olive oil, half of the sea salt, and half of the black pepper.
Mince the garlic cloves and whisk them in a small bowl with the remaining olive oil, rosemary, thyme, and the rest of the salt and pepper.
Pat the chicken breast dry with a paper towel and rub the garlic-herb oil mixture thoroughly over all sides of the meat.
Spread the seasoned vegetables across the prepared baking sheet and nestle the chicken breast in the center, ensuring everything is in a single layer.
Roast in the center of the oven for 20 to 25 minutes, or until the chicken reaches an internal temperature of 165°F and the sweet potatoes are fork-tender.
Remove from the oven and let the chicken rest for 5 minutes to lock in the juices before slicing and serving alongside the roasted vegetables.