Rinse quinoa under cold water until clear. Combine quinoa with water or broth in a saucepan. Bring to a boil, then reduce heat, cover, and simmer for 15 minutes. Remove from heat and let sit, covered, for 5 minutes before fluffing with a fork.
Preheat oven to 400°F (200°C). Toss chopped bell pepper, zucchini, and red onion with 1 tablespoon olive oil, salt, and pepper on a baking sheet. Roast for 20-25 minutes until tender.
If using chicken: Pat chicken dry, season with salt, pepper, and oregano. Heat 1 teaspoon olive oil in a skillet over medium-high heat. Cook chicken for 6-8 minutes per side until cooked through. Let rest, then slice or dice. If using chickpeas: Drain and rinse; optionally pan-fry lightly with paprika.
In a large bowl, combine cooked quinoa, roasted vegetables, protein (chicken or chickpeas), halved cherry tomatoes, chopped cucumber, feta (if using), fresh parsley, and fresh mint.
In a small bowl, whisk together remaining 2 tablespoons olive oil, lemon juice, minced garlic, dried oregano, salt, and pepper to create the dressing. Pour over the bowl ingredients and toss gently to combine. Serve immediately.