Add the chickpeas to a bowl and toss with olive oil and za’atar.
Lay the chickpeas out on the sheet pan in a single layer and roast for 20–25 minutes, until golden and slightly crisp.
Meanwhile, make the dressing. In a blender, add the Greek yogurt, grated cucumber, olive oil, lemon juice, garlic, dill, salt, and pepper. Blend until smooth.
Assemble the salad: In a large bowl, combine the chopped cucumber, tomatoes, red onion, feta, olives, and parsley.
Top the salad with the roasted chickpeas.
To serve, spoon the tzatziki dressing over the salad or serve on the side.