In a bowl, mix Greek yogurt, olive oil, lemon juice, garlic, shallots, paprika, oregano, and pepper flakes. Coat chicken and marinate for at least 15 minutes or overnight for deeper flavor.
Preheat oven to 425°F. Spread sliced bell peppers on a sheet pan with olive oil, salt, and pepper. Roast 18–20 minutes until tender and slightly charred.
Place marinated chicken on another pan and bake for 15 minutes. Stir, then cook another 5–10 minutes until golden and fully cooked.
Switch to broil and cook chicken for 1–2 minutes to lightly char the edges.
Blend feta, ¼ cup yogurt, garlic, and lemon juice until smooth. Stir in remaining yogurt, cucumber, salt, and optional pepper flakes.
Warm pitas, spread tzatziki inside, add lettuce, chicken, roasted peppers, and pickled onions. Top with fresh herbs and extra sauce.
