Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Peel the sweet potato and cut it into 1-inch cubes, and slice the carrots into rounds.
Toss the sweet potatoes and carrots on the baking sheet with half of the olive oil, half of the sea salt, and half of the black pepper.
Roast the sweet potatoes and carrots for 10 minutes.
While the vegetables roast, mince the garlic and combine it in a small bowl with the remaining olive oil, rosemary, thyme, salt, and pepper.
Rub the herb mixture evenly over the chicken breast.
Remove the baking sheet from the oven, move the potatoes and carrots to one side, and add the chicken breast and broccoli florets to the other side.
Return the sheet to the oven and roast for an additional 18-22 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender.
Allow the chicken to rest for 5 minutes before slicing to ensure it remains juicy.