Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Scrub the russet potato clean and dice it into 1/2-inch cubes for even cooking.
Mince the garlic clove and place it in a large mixing bowl with the olive oil, rosemary, sea salt, and black pepper.
Add the diced potatoes and the chicken breast to the bowl, tossing thoroughly to ensure everything is coated in the herb oil.
Spread the potatoes and chicken onto the prepared baking sheet in a single layer, ensuring they aren't crowded.
Roast in the oven for 15 minutes.
While the chicken roasts, lightly mist the broccoli florets with a tiny bit of water or oil.
Remove the sheet pan, flip the potatoes, and add the broccoli florets to the tray.
Return to the oven for another 10-12 minutes until the chicken reaches an internal temperature of 165°F and the potatoes are tender.
Let the chicken rest for 5 minutes before slicing to keep it juicy, then serve alongside the roasted vegetables.