Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper for easy cleanup.
Peel and dice the sweet potato into 1/2-inch cubes, and finely mince the garlic cloves and fresh rosemary.
In a small bowl, whisk together 0.5 tablespoon of olive oil, the minced garlic, rosemary, dried oregano, and half of the salt and pepper.
Place the chicken breast on one side of the baking sheet and rub the garlic-herb oil mixture thoroughly over both sides.
In a separate bowl, toss the sweet potato cubes and broccoli florets with the remaining 0.25 tablespoon of olive oil and the rest of the salt and pepper.
Spread the vegetables in a single layer on the other side of the baking sheet, ensuring they aren't overcrowded so they roast rather than steam.
Roast in the center of the oven for 20-25 minutes, or until the chicken reaches an internal temperature of 165°F and the sweet potatoes are golden and tender.
Remove from the oven and let the chicken rest for 5 minutes before slicing to ensure the juices stay locked in.