Preheat your oven to 400°F and heat an outdoor grill or indoor grill pan to medium-high heat.
Toss the broccoli florets with half of the olive oil, salt, and pepper on a baking sheet and roast for 15-20 minutes until the edges are charred.
In a small saucepan, combine the dry quinoa with 1 cup of water, bring to a boil, then cover and simmer for 15 minutes until the water is absorbed and the quinoa is fluffy.
In a small bowl, whisk together the remaining olive oil, lemon juice, minced garlic, and a pinch of dried oregano.
Brush the turkey breast with the lemon-garlic mixture and grill for 5-7 minutes per side, or until the internal temperature reaches 165°F.
Let the turkey rest for 5 minutes before slicing it into strips.
Serve the sliced turkey over the cooked quinoa with the roasted broccoli on the side.