Preheat your oven to 400°F (200°C) and line a large sheet pan with parchment paper.
Dice the Yukon Gold potato into 1/2-inch cubes and place them in a bowl.
Toss the potatoes with half of the olive oil, half of the sea salt, and half of the black pepper.
Spread the potatoes onto the prepared baking sheet and roast for 15 minutes.
While the potatoes roast, mince the garlic and whisk it together with the remaining olive oil, lemon juice, rosemary, and thyme.
Pat the chicken breast dry and coat it thoroughly with the lemon-herb mixture and remaining salt and pepper.
Remove the sheet pan from the oven, move the potatoes to one side, and add the chicken breast and broccoli florets to the other side.
Return the pan to the oven and roast for another 18-22 minutes, or until the chicken reaches an internal temperature of 165°F and the potatoes are golden and crisp.
Let the chicken rest for 5 minutes before slicing to keep it juicy.