Mellow the Onions: Place the thinly sliced red onion in a large mixing bowl. Pour the red wine vinegar and fresh lemon juice directly over the onions. Stir briefly and set aside for at least 10 minutes to marinate; this will soften their sharp bite.
Craft the Vinaigrette: In a small jar with a tight-fitting lid, combine the extra-virgin olive oil, minced garlic, dried oregano, Dijon mustard, and black pepper. Seal the jar tightly and shake vigorously for 30 seconds until the dressing is well-combined and slightly thickened (emulsified).
Combine the Vegetables: To the mixing bowl with the marinating onions, add the sliced Persian cucumbers, chopped yellow bell pepper, and halved cherry tomatoes.
Integrate Core Ingredients: Add the rinsed chickpeas and halved Kalamata olives to the vegetable medley in the bowl.
Dress and Assemble: Pour the emulsified vinaigrette from the jar over the salad ingredients. Toss gently with tongs or large spoons until everything is evenly coated. Add the cubed feta cheese and toss once or twice more, being careful not to break up the cheese.
Garnish and Serve: Transfer the salad to a large serving platter. Garnish generously with the torn fresh mint and chopped parsley. For the best texture and flavor, serve immediately.