Preheat your oven to 425°F (220°C) and line a large sheet pan with parchment paper or lightly grease it.
Slice the lemon in half. Using one half, extract the juice and set aside. Reserve a few thin slices from the other half for garnish if desired.
In a small bowl, combine the olive oil, minced garlic, and lemon juice. Season with a pinch of salt and freshly ground black pepper.
Place the chicken breast on one side of the sheet pan. Brush the chicken generously with the lemon garlic mixture.
In a separate bowl, toss the broccoli florets with a drizzle of olive oil, the remaining minced garlic (if desired), a squeeze of lemon juice, salt, and pepper.
Arrange the broccoli on the sheet pan around the chicken, ensuring they are in a single layer for even roasting.
Bake in the preheated oven for 20-25 minutes or until the chicken is cooked through (internal temperature of 165°F) and the broccoli edges are crispy and lightly charred.
Remove from the oven, garnish with fresh lemon slices if using, and serve immediately.