Preheat your oven to 400°F and line a large sheet pan with parchment paper.
Scrub the yellow potato and cut it into 1-inch cubes, then finely mince the garlic cloves.
In a medium bowl, toss the potato cubes with half of the olive oil, half of the minced garlic, dried rosemary, dried thyme, sea salt, and black pepper.
Spread the potatoes in a single layer on the sheet pan and roast for 15 minutes.
While potatoes roast, brush the chicken breast with the remaining olive oil and minced garlic, and season with a small pinch of salt and pepper.
Move the potatoes to one side of the pan, add the chicken breast and broccoli florets to the other side, and roast for an additional 18-20 minutes until the chicken is cooked through.
Remove the pan from the oven and finish the meal with a fresh squeeze of lemon juice over the chicken and vegetables before serving.