Preheat your oven to 400°F and line a large rimmed baking sheet with parchment paper.
Wash the potato and dice it into 1-inch cubes, then chop the broccoli into bite-sized florets.
In a small bowl, whisk together the olive oil, minced garlic, rosemary, thyme, sea salt, and black pepper.
Place the chicken breast, potato cubes, and broccoli florets in a large mixing bowl and drizzle with the garlic-herb oil.
Toss everything thoroughly until the chicken and vegetables are evenly coated in the herb mixture.
Spread the ingredients in a single layer on the prepared baking sheet, ensuring the potatoes have enough space to crisp up.
Roast for 22-25 minutes, or until the chicken reaches an internal temperature of 165°F and the potatoes are fork-tender and golden brown.
Remove from the oven and let the chicken rest for 5 minutes before slicing and serving alongside the roasted vegetables.