Preheat your oven to 400°F (200°C) and line a large sheet pan with parchment paper.
Mince the garlic cloves and finely chop the fresh rosemary needles.
Slice the carrots into half-inch rounds and cut the baby potatoes into halves or quarters so they are uniform in size.
In a large mixing bowl, combine the chicken breast, potatoes, and carrots.
Drizzle with extra virgin olive oil and add the minced garlic, chopped rosemary, sea salt, and black pepper.
Toss everything thoroughly until the chicken and vegetables are evenly coated in the oil and aromatics.
Spread the mixture onto the prepared baking sheet in a single layer, ensuring the chicken pieces are not crowded.
Roast in the center of the oven for 15 minutes.
Remove the pan briefly to toss the vegetables and add the broccoli florets to the sheet.
Return to the oven and roast for an additional 10 to 15 minutes, or until the chicken reaches an internal temperature of 165°F and the potatoes are golden.
Squeeze the juice of the half lemon over the entire pan before serving to brighten the flavors.