In a jar or container with a tight-fitting lid, combine the olive oil, white wine vinegar, lemon juice, red pepper flakes, and dried oregano. Seal the lid and shake vigorously for 15-20 seconds until the ingredients are well emulsified and the oregano is fully incorporated. Taste the dressing and season with a pinch of salt and black pepper. Set aside while you prepare the vegetables. I find making the dressing first allows the flavors to meld while you work on chopping, giving you a more cohesive sauce by the time you need it.
While the dressing flavors develop, prepare all the vegetables with consistent sizing for even distribution throughout the salad. Dice the cucumber into 1/2-inch pieces, dice the red bell pepper into 1/2-inch pieces, and thinly slice or finely dice the red onion. Drain and rinse the chickpeas thoroughly under cold water until the water runs clear—this removes excess starch and prevents the salad from becoming gummy. Pit and halve the olives. Crumble the feta cheese into bite-sized pieces. Having everything prepped and ready makes assembly quick and ensures consistent texture throughout.
In a large bowl, combine the prepared chickpeas, cucumber, bell pepper, red onion, feta cheese, and olives. Pour the dressing from Step 1 over the salad and toss gently but thoroughly until all components are evenly coated. Taste and adjust seasoning with additional salt and black pepper as needed. Stir in the freshly chopped parsley just before serving to maintain its bright, fresh flavor rather than letting it wilt in the dressing.