Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Scrub the sweet potato and cut it into 1-inch cubes, then toss them in a bowl with half of the olive oil and a pinch of salt.
Spread the sweet potato cubes onto the baking sheet and roast for 10 minutes to give them a head start.
While the potatoes roast, mince the garlic and whisk it in a small bowl with the remaining olive oil, rosemary, thyme, salt, pepper, and lemon juice.
Pat the chicken breast dry with a paper towel and rub the garlic-herb mixture thoroughly over all sides.
Remove the baking sheet from the oven, slide the potatoes to one side, and place the chicken breast on the other side.
Return the pan to the oven and roast for 20-25 minutes, or until the chicken reaches an internal temperature of 165°F.
While the chicken and potatoes finish roasting, steam the broccoli florets in a steamer basket over boiling water for 5 minutes until tender-crisp.
Remove the pan from the oven and let the chicken rest for 5 minutes to ensure the juices redistribute.
Slice the chicken and serve immediately alongside the caramelized sweet potatoes and steamed broccoli.