Preheat your oven to 400°F (200°C) and line a large sheet pan with parchment paper.
Wash and cube the red potato into 1/2-inch pieces and slice the carrots into rounds.
In a small bowl, whisk together the olive oil, minced garlic, chopped rosemary, and chopped thyme.
Toss the potatoes and carrots on the sheet pan with one-third of the herb-oil mixture and a pinch of salt and pepper; roast for 10 minutes.
While the root vegetables pre-roast, chop the broccoli into florets, slice the red onion, and dice the bell pepper.
Rub the chicken breast with half of the remaining herb-oil mixture and the rest of the salt and pepper.
Remove the pan from the oven, push the potatoes and carrots to the side, and place the chicken breast in the center.
Add the broccoli, onion, and bell pepper to the pan, drizzling them with the last of the herb oil.
Return the pan to the oven and roast for 18-22 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender.
Let the chicken rest for 5 minutes before slicing to ensure it stays juicy, then serve immediately.