Preheat your oven to 400°F and line a large rimmed baking sheet with parchment paper.
Peel the sweet potato and cut into 1/2-inch cubes, then toss them on the baking sheet with half of the olive oil, salt, and pepper.
Roast the sweet potatoes for 10 minutes to give them a head start.
In a small glass bowl, whisk together the honey, Dijon mustard, apple cider vinegar, and garlic powder until the glaze is smooth and emulsified.
Pat the chicken breast dry with a paper towel and season both sides with the remaining salt and pepper.
Move the sweet potatoes to one side of the pan, then add the chicken breast and broccoli florets to the other side.
Drizzle the broccoli with the remaining olive oil and brush half of the honey-mustard glaze over the chicken breast.
Return the pan to the oven and roast for 15-18 minutes, or until the chicken reaches an internal temperature of 165°F.
Remove from the oven and drizzle the remaining honey-mustard sauce over both the chicken and the roasted sweet potatoes before serving.