Preheat your oven to 400°F (200°C) and prepare a grill or grill pan over medium-high heat.
In a small bowl, whisk together 0.5 tablespoon of olive oil, lemon juice, and minced garlic.
Place the chicken breast in a shallow dish and coat with the lemon-garlic mixture, letting it marinate for at least 10 minutes.
Toss the broccoli florets with the remaining 1 tablespoon of olive oil, salt, and pepper on a baking sheet.
Roast the broccoli in the oven for 15-20 minutes until the edges are tender and slightly charred.
While the broccoli roasts, place the chicken on the grill and cook for 6-7 minutes per side, or until the internal temperature reaches 165°F.
Warm the pre-cooked quinoa in a small saucepan or microwave until heated through.
Plate the grilled chicken alongside the fluffy quinoa and roasted broccoli, garnishing with extra lemon if desired.