Stage 1: Aromatic Vinaigrette Emulsification: In the small bowl or jar, combine the minced garlic, lemon juice, lemon zest, red wine vinegar, dried oregano, and black pepper. Whisk vigorously while slowly drizzling in the extra-virgin olive oil until slightly thickened. Set aside.
Stage 2: Salad Component Integration: In the large mixing bowl, add the rinsed chickpeas, diced cucumber, halved tomatoes, diced bell pepper, sliced red onion, and sliced olives. Pour the prepared vinaigrette over the vegetables and toss gently until lightly coated.
Stage 3: Marination & Flavor Infusion: Gently fold the crumbled reduced-fat feta into the salad mixture. Set aside to marinate for at least 10 minutes while you prepare the wraps.
Stage 4: Fortified Wrap Batter Creation: In a separate medium bowl, whisk the egg whites until frothy and uniform, about 30 seconds. Add the whole wheat flour, ground flaxseed, za'atar, and fresh parsley. Whisk until smooth.
Stage 5: Skillet-Forging the Wraps: Place the 10-inch nonstick skillet over medium-low heat and lightly coat with cooking spray or a few drops of oil if needed. Once warm, pour one-quarter of the batter (about 3/8 cup / 90 ml) into the center, swirling to form an even, thin circle. Cook 2–3 minutes, until the edges are set and the top is mostly opaque.
Stage 6: Final Cooking & Assembly: Cover and cook 1–2 minutes more, until the wrap is fully set, opaque, and pliable with no wet spots. Slide onto a plate and repeat with the remaining batter to make four wraps. Using a slotted spoon, place one-quarter of the marinated chickpea filling (leaving excess liquid behind) down the center of each wrap, fold the sides over, and serve immediately.