Preheat your oven to 425°F.
In a small bowl, combine the juice of half a lemon with 2 minced garlic cloves, a pinch of salt, and black pepper.
Pat the chicken breast dry and rub half of the lemon-garlic mixture over it. Let it marinate for 10 minutes.
On a medium skillet, heat 1/2 tablespoon of olive oil over medium-high heat. Sear the chicken breast for about 3-4 minutes on each side until a golden crust forms.
Meanwhile, toss the broccoli with the remaining olive oil, a pinch of salt, and pepper. Spread it out on a baking sheet.
Place the broccoli in the preheated oven and roast for 12-15 minutes until tender and slightly crispy on the edges.
After searing, reduce the heat on the skillet to medium-low, cover, and let the chicken cook through for an additional 5-7 minutes.
Plate the chicken and roasted broccoli, drizzle any remaining pan juices over the chicken, and garnish with a final squeeze of fresh lemon juice.