Rinse the quinoa under cold water to remove any impurities. In a medium pot, combine the quinoa and water. Bring to a boil, then reduce heat to low, cover, and simmer for 15 minutes or until the water is absorbed. Remove from heat, fluff with a fork, and let cool slightly.
In a large bowl, combine the cooled quinoa, diced cucumber, chopped parsley, chopped mint, finely chopped red onion, chopped pistachios, and drained chickpeas.
In a small bowl, whisk together the lemon juice, olive oil, salt, and pepper. Pour the dressing over the salad and toss to combine.
Gently fold in the crumbled feta cheese.
Serve the salad immediately, or for enhanced flavor, let it chill in the refrigerator for a few hours before serving.