Rinse quinoa in a fine-mesh sieve under cool running water for 30 to 60 seconds, then drain well.
Combine quinoa, water and salt in a saucepan. Bring to a boil, cover, reduce to low and simmer 14 to 17 minutes until the water is absorbed.
Remove from heat and rest covered for 5 minutes. Fluff, spread on a rimmed pan, and cool for about 15 minutes so steam escapes.
Whisk olive oil, lemon juice, Dijon, garlic, oregano and pepper until lightly emulsified.
Add cool quinoa, chickpeas, cucumber, tomatoes, parsley and onion to a large bowl. Toss with about three-quarters of the dressing.
Fold in feta if using, rest for 5 minutes, and add only enough remaining dressing to make the salad bright but not wet.