In a mixing bowl, combine yogurt, olive oil, garlic, shallots, paprika, oregano, chili flakes, salt, and pepper. Add chicken and toss to coat. Marinate for 15 minutes or overnight.
Preheat oven to 425°F. Spread marinated chicken on a baking sheet. Roast for 15–20 minutes. Broil for 1–2 minutes to char edges.
While chicken cooks, prepare the tzatziki by mixing Greek yogurt, grated cucumber (squeeze excess water), garlic, lemon juice, dill, salt, and pepper.
In a blender, combine tahini, ginger, lemon juice, garlic, tamari, and honey. Blend until smooth, adding water to thin if necessary. Season with salt.
Toss cucumber, avocado, lemon juice, dill, salt, and pepper in a bowl to make the cucumber avocado salad.
Assemble bowls by layering shredded lettuce, chicken, cucumber avocado salad, crumbled feta, peperoncini, and tomatoes. Top with dollops of tzatziki and a drizzle of ginger tahini sauce.
Serve with warm pita or naan.