In a medium saucepan, combine quinoa and water or chicken broth. Bring to a boil, then reduce heat to low, cover, and simmer for 15 minutes or until quinoa is cooked and liquid is absorbed. Fluff with a fork and let it cool.
In a small bowl, whisk together olive oil, red wine vinegar, lemon juice, honey, minced garlic, dried oregano, salt, and black pepper. Set aside.
In a large mixing bowl, combine cooked quinoa, shredded roasted chicken, cherry tomatoes, cucumber, red onion, Kalamata olives, feta cheese, and chopped parsley.
Pour the lemon-herb vinaigrette over the salad ingredients. Toss gently to coat everything evenly.
Transfer the salad to a serving platter or individual plates. Garnish with additional feta cheese and parsley if desired.