In a bowl, combine Greek yogurt, olive oil, lemon juice, garlic, shallot, smoked paprika, oregano, salt, and black pepper. Toss the chicken pieces in this marinade until fully coated. I like letting the chicken sit for at least 10 minutes so the flavors really sink in.
Spread the marinated chicken on a sheet pan in a single layer. Roast in a preheated oven at 425°F (220°C) for 20-25 minutes or until slightly charred and fully cooked. This gives the chicken that delicious, roasted flavor without extra fuss.
In a blender or food processor, combine feta cheese, Greek yogurt, lemon juice, garlic, and olive oil. Blend until creamy, then stir in diced cucumbers and chili flakes. This sauce is the real star—creamy, tangy, and packed with flavor.
Warm the pita bread in the oven for a few minutes. Spread a generous layer of feta tzatziki on the bread, add roasted chicken, and top with fresh herbs, extra cucumbers, or a drizzle of harissa. Fold and enjoy immediately.