Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper for easy cleanup.
Scrub the Yukon Gold potato and dice it into uniform 1-inch cubes to ensure even cooking.
Mince the garlic cloves and finely chop the fresh rosemary leaves.
In a large bowl, toss the potato cubes with 0.5 tbsp of the olive oil, half of the minced garlic, half of the rosemary, and a pinch of the sea salt and black pepper.
Spread the potatoes in a single layer on the prepared baking sheet and roast for 15 minutes.
While the potatoes roast, rub the chicken breast with the remaining 0.25 tbsp of olive oil, the rest of the garlic, rosemary, sea salt, and black pepper.
Remove the baking sheet from the oven, push the potatoes to one side, and place the chicken breast and broccoli florets on the other side.
Return the sheet to the oven and roast for an additional 18-20 minutes, or until the chicken reaches an internal temperature of 165°F and the potatoes are golden-brown.
Let the chicken rest for 5 minutes before slicing to ensure the meat remains juicy and tender.