Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper for easy cleanup.
Peel the sweet potato and carrots, then dice the potato into 1-half inch cubes and slice the carrots into rounds.
In a large mixing bowl, toss the sweet potatoes and carrots with 0.5 tablespoon of olive oil, half of the sea salt, and half of the black pepper.
Spread the potatoes and carrots onto the prepared baking sheet and roast for 10 minutes.
While the vegetables begin roasting, pat the chicken breast dry and rub with 0.5 tablespoon of olive oil, rosemary, thyme, and garlic powder.
Remove the pan from the oven, move the potatoes and carrots to one side, and place the chicken breast in the center.
Add the broccoli florets to the remaining open space on the pan, drizzling them with the final 0.5 tablespoon of olive oil and the remaining salt and pepper.
Return the pan to the oven and roast for another 18-22 minutes until the chicken reaches an internal temperature of 165°F and the vegetables are tender.
Remove from the oven and let the chicken rest for 5 minutes before slicing to ensure maximum juiciness.