Preheat your oven to 400°F and line a large baking sheet with parchment paper for easy cleanup.
Dice the sweet potato into 1/2-inch cubes and slice the carrots into thin rounds to ensure even cooking.
In a small glass bowl, whisk together the extra virgin olive oil, minced garlic, chopped rosemary, thyme, sea salt, and black pepper.
Place the chicken breast, sweet potato cubes, and carrot rounds on the prepared baking sheet.
Drizzle three-quarters of the herb oil over the chicken and vegetables, tossing well to ensure every piece is thoroughly coated.
Roast in the center of the oven for 15 minutes, then remove the tray to add the broccoli florets and drizzle them with the remaining oil.
Return the tray to the oven and roast for another 10 to 12 minutes until the chicken reaches an internal temperature of 165°F and the vegetables are golden brown.
Allow the chicken to rest for 5 minutes before slicing to keep it juicy, then serve immediately alongside the roasted vegetables.