Preheat your oven to 400°F (200°C) and line a rimmed baking sheet with parchment paper.
In a small mixing bowl, whisk together the olive oil, minced garlic, rosemary, thyme, sea salt, black pepper, and the juice of the half lemon.
Pat the chicken breast completely dry with a paper towel to ensure the skin gets crispy, then place it on one side of the baking sheet.
Place the broccoli florets on the other side of the baking sheet and drizzle them with one-third of the lemon-herb oil mixture, tossing to coat.
Brush the remaining lemon-herb oil generously over both sides of the chicken breast.
Roast in the center of the oven for 20-25 minutes, or until the chicken reaches an internal temperature of 165°F and the broccoli is tender and slightly charred.
Remove from the oven and let the chicken rest for 5 minutes before slicing to ensure it remains juicy.