Place the red onion in a large mixing bowl.
In a small jar with a tight-fitting lid, combine olive oil, red wine vinegar, lemon juice, garlic, oregano, Dijon, and black pepper. Shake vigorously for 30 seconds until emulsified.
Spoon 1–2 tablespoons of the vinaigrette over the onions, toss, and let sit for 10 minutes.
Add cucumbers, yellow bell pepper, and tomatoes to the bowl.
Add chickpeas and Kalamata olives.
Pour the remaining vinaigrette over the salad and toss gently until evenly coated.
Add the cubed feta and toss once or twice more, taking care not to break it up.
Transfer to a serving platter, garnish with mint and parsley, and let sit 10 minutes before serving.