Make the tzatziki first: Grate half a large cucumber on the coarse side of a grater. Squeeze out excess water using a clean towel or paper towels until mostly dry. In a bowl, mix Greek yogurt, grated cucumber, minced garlic, chopped dill, a squeeze of lemon, a drizzle of olive oil, salt, and pepper.
Taste and adjust with more lemon or salt. Chill while you prep everything else.
Prep the veggies: Slice the remaining cucumber into half-moons, chop tomatoes, thinly slice red onion, and wash and dry your greens. Chop parsley and extra dill.
If using olives or roasted red peppers, slice them.
Season the chickpeas: Pat the chickpeas dry with a towel for better browning. In a bowl, toss chickpeas with olive oil, 1 teaspoon cumin, 1 teaspoon smoked paprika, 1 teaspoon dried oregano, 1/2 teaspoon garlic powder, 1/2 teaspoon salt, black pepper to taste, and a pinch of red pepper flakes if you like heat.
Crisp the chickpeas: Heat a large skillet over medium-high. Add chickpeas and cook 6–8 minutes, shaking occasionally, until lightly crisp and fragrant.
Finish with a squeeze of lemon and a pinch more salt. For extra texture, let them sit undisturbed for a minute at a time to sear.
Warm the wraps: In a dry pan or directly over a low gas flame, warm pitas or tortillas until soft and pliable. Keep them stacked under a clean towel to stay warm.
Assemble: Spread a generous layer of tzatziki over each wrap.
Add a handful of greens, a scoop of chickpeas, cucumber, tomato, and onion. Sprinkle with chopped herbs and crumbled feta. Add olives or peppers if using.
Finish and fold: Add a light drizzle of olive oil and a squeeze of lemon.
Fold the sides in and roll tightly, or fold like a taco if using smaller pitas. Serve immediately while warm.