Cook the quinoa: In a medium saucepan, combine rinsed quinoa and water or broth. Bring to a boil, then reduce heat to low, cover, and simmer for 15 minutes, or until liquid is absorbed. Remove from heat and let sit covered for 5 minutes, then fluff with a fork. Spread on a baking sheet to cool quickly.
While quinoa cooks, prepare the cucumber: Place diced cucumber in a colander, sprinkle with a pinch of salt, and let sit for 10 minutes to draw out excess water. Pat dry with paper towels.
In a large bowl, combine cooled quinoa, cucumber, red onion, parsley, mint, and dill.
In a small bowl, whisk together lemon juice, olive oil, salt, and pepper. Pour over the salad and toss gently to combine.
If using, fold in feta cheese or chickpeas. Taste and adjust seasoning with more salt, pepper, or lemon juice as needed.
Let the salad rest for at least 10 minutes before serving to allow flavors to meld. Serve at room temperature or chilled.