Preheat your oven to 400°F (200°C) and line a large sheet pan with parchment paper for easy cleanup.
Wash and halve the baby potatoes, and chop the broccoli into uniform bite-sized florets.
Mince the garlic clove and finely chop the fresh thyme and rosemary leaves.
On the sheet pan, toss the halved potatoes with half of the olive oil, half of the sea salt, and half of the black pepper.
Spread the potatoes in a single layer and roast for 10 minutes to give them a head start.
While the potatoes roast, zest and juice the half lemon into a small bowl.
Whisk the remaining olive oil, lemon zest, lemon juice, minced garlic, thyme, and rosemary together.
Pat the chicken breast dry and coat it thoroughly with the lemon-herb mixture.
Remove the pan from the oven, move the potatoes to one side, and place the chicken and broccoli florets on the other side.
Season the broccoli with the remaining salt and pepper, then return the pan to the oven.
Roast for an additional 15 to 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 keep it juicy, then serve immediately.