Rinse the quinoa in a fine-mesh strainer under cold water for about 1 minute. Drain well.
In a medium saucepan, heat 1 tablespoon of the olive oil over medium heat. Add the rinsed quinoa and cook, stirring constantly, for 2 to 3 minutes, until it smells nutty and has a light toasty flavor.
Add the water or vegetable broth to the saucepan with the quinoa. Bring to a boil, then reduce heat to low, cover, and simmer for 15 minutes or until quinoa is tender and water is absorbed.
While the quinoa simmers, chop the English cucumber, halve the cherry tomatoes, and finely dice the red onion.
In a separate bowl, mix the lemon juice, oregano, salt, and pepper. Slowly add the remaining 1 tablespoon of olive oil to the quinoa, stirring constantly to avoid clumping.
When the quinoa is cool, remove it from heat and transfer it to a large mixing bowl. Add the diced cucumber, halved cherry tomatoes, finely diced red onion, halved kalamata olives, and crumbled feta cheese to the bowl with the quinoa.
Stir in the chopped parsley and drizzle with the lemon-herb dressing. Mix gently to combine all ingredients.
Cover the bowl with plastic wrap and let it sit for at least 15 minutes to allow the flavors to meld. Serve at room temperature.