Preheat your oven to 400°F (200°C) and line a large sheet pan with parchment paper for easy cleanup.
Peel the sweet potato and cut it into 1-inch cubes, then place them on the prepared baking sheet.
In a small mixing bowl, whisk together the olive oil, lemon zest, lemon juice, minced garlic, rosemary, thyme, salt, and pepper.
Pat the chicken breast dry with a paper towel and place it on the pan; brush half of the herb-oil mixture over both sides of the chicken.
Add the broccoli florets and sliced carrots to the pan with the sweet potatoes, drizzle with the remaining herb-oil mixture, and toss to coat.
Spread the vegetables in a single layer around the chicken to ensure even roasting and maximum crispness.
Roast for 20 to 25 minutes, or until the chicken reaches an internal temperature of 165°F and the sweet potatoes are fork-tender.
Allow the chicken to rest for 5 minutes before slicing to keep the juices intact, then serve immediately with the roasted vegetables.