Preheat your oven to 400°F and line a baking sheet with parchment paper.
Toss the broccoli florets with half of the olive oil, salt, and pepper on the prepared baking sheet.
Roast the broccoli for 15-20 minutes until the edges are slightly charred and tender.
Rinse the quinoa in a fine-mesh sieve and place in a small pot with 1/2 cup of water.
Bring the quinoa to a boil, then reduce heat to low, cover, and simmer for 12-15 minutes until the water is absorbed.
Whisk together the remaining olive oil, lemon juice, and minced garlic in a small bowl to create a marinade.
Brush the chicken breast with the lemon-garlic mixture and season both sides with salt and pepper.
Grill the chicken over medium-high heat for 6-7 minutes per side or until the internal temperature reaches 165°F.
Let the chicken rest for 5 minutes before slicing, then serve alongside the fluffed quinoa and roasted broccoli.