Preheat oven to 425 degrees F. On a small baking sheet, toss diced zucchini and halved cherry tomatoes with olive oil and season with salt, pepper, and 1 teaspoon za'atar spice.
On another baking pan, use a paper towel to pat dry the chickpeas before tossing them with olive oil, paprika, and salt and pepper.
Place both vegetables and chickpeas into the oven and bake for 16 minutes or until vegetables are slightly browned and softened and the chickpeas are crispy.
Meanwhile, heat olive oil over medium-low heat in a frying pan. Season diced chicken with za'atar spice, salt, and pepper. Add to the frying pan and cook until cooked through flipping after 5 minutes.
While the chicken cook, mash feta until in small pieces using a fork. Then combine with sour cream and lemon zest. Add a little bit of water at a time until the sauce is thinned and able to be drizzled.
Once everything is cooked, layer in a pita or tortilla hummus, lettuce, seasoned chicken, roasted vegetables, chickpeas, feta, and feta sauce. Enjoy!