Preheat your oven to 400°F and line a large baking sheet with parchment paper for easy cleanup.
Scrub the potato and cut it into 1-inch cubes to ensure they roast evenly with the chicken.
Mince the garlic clove finely and set it aside.
In a large mixing bowl, toss the potato cubes and broccoli florets with half of the olive oil, sea salt, and black pepper.
Rub the chicken breast with the remaining olive oil, minced garlic, dried rosemary, and dried thyme until thoroughly coated.
Arrange the chicken and potatoes on the prepared baking sheet in a single layer, leaving space for air to circulate.
Roast for 15 minutes, then carefully flip the potatoes and add the broccoli florets to the sheet.
Continue roasting for another 10 to 15 minutes until the chicken reaches an internal temperature of 165°F and the potatoes are golden and tender.