Preheat your oven to 400°F and line a large rimmed baking sheet with parchment paper.
Scrub the potato clean and cut it into 1/2-inch cubes, then finely mince the garlic cloves.
Place the potato cubes on the baking sheet, drizzle with 0.5 tbsp of olive oil, and toss with half of the minced garlic, sea salt, black pepper, and dried rosemary.
Spread the potatoes in a single layer and roast for 15 minutes.
While the potatoes are roasting, rub the chicken breast with the remaining 0.25 tbsp of olive oil and the rest of the garlic, salt, pepper, and rosemary.
Remove the baking sheet from the oven, slide the potatoes to one side, and place the chicken breast and broccoli florets on the other side.
Return the pan to the oven and roast for another 15-20 minutes until the chicken reaches an internal temperature of 165°F and the potatoes are crispy.
Allow the chicken to rest for 5 minutes before slicing it into strips and serving alongside the roasted potatoes and broccoli.