Preheat the oven to 425°F. Toss the broccoli, bell pepper, and zucchini with 1 tablespoon olive oil, half the minced garlic, and a pinch of salt and pepper on a baking sheet. Roast for 20 minutes until the edges start to brown.
While the vegetables roast, stir together the lemon juice, lemon zest, remaining garlic, 2 tablespoons olive oil, salt, and pepper in a bowl. Add the chicken breasts and turn to coat evenly. Let them sit while you start the quinoa.
Bring 2 cups of water to a boil in a saucepan. Add the rinsed quinoa, cover, and simmer on low for 15 minutes until the water is absorbed. Remove from heat and let it rest covered for 5 minutes, then fluff with a fork.
Heat a grill or grill pan over medium-high heat. Grill the chicken for 5 to 6 minutes per side until it reaches an internal temperature of 165°F. Let the chicken rest for 3 minutes, then slice it.
Divide the quinoa among four bowls. Top each with roasted vegetables and sliced chicken. Sprinkle with fresh parsley before serving.