In a large bowl, combine the yogurt, olive oil, minced garlic, minced shallots, paprika, oregano, chili flakes, cayenne pepper, salt, black pepper, and red wine vinegar. Add the bite-sized chicken pieces and toss until evenly coated with the marinade. Let sit at room temperature for at least 15 minutes while you prepare the remaining components. I like to marinate for at least 30 minutes when I have time—the longer the chicken sits, the more the flavors penetrate and the more tender the meat becomes.
While the chicken marinates, prepare your tahini sauce by blending the tahini, minced garlic, grated ginger, tamari, lemon juice, and honey with 1/4 cup water until smooth and creamy—add more water if needed to reach a pourable consistency. In a separate bowl, combine the diced cucumbers, diced avocado, lemon juice, chopped fresh dill, salt, and black pepper for the fresh vegetable component. Prepare your remaining fresh ingredients: shred the lettuce, thinly slice the red onion into half-moons, dice the tomatoes, and slice the peperoncini. Crumble the feta cheese into bite-sized pieces.
Preheat your oven to 425°F. Spread the marinated chicken pieces in a single layer on a sheet pan, making sure they're not crowded. Roast for 15 minutes until the chicken is mostly cooked through. Flip the pieces and roast for another 5-10 minutes until the internal temperature reaches 165°F. For a nice charred finish, turn on the broiler and broil for 1-2 minutes until you get some caramelization on the edges—watch carefully to avoid burning. I like to arrange the chicken pieces cut-side up on the pan before the final broil so they get maximum char on the most visible surface.
Divide the shredded lettuce evenly among four bowls or pita pockets as your base. Top each with a portion of the roasted chicken from Step 3, then add the fresh cucumber and avocado mixture from Step 2. Distribute the sliced red onion, diced tomatoes, peperoncini, and crumbled feta evenly across the bowls. Drizzle each bowl generously with both the tahini sauce from Step 2 and the tzatziki sauce. Serve with warm pita bread on the side for scooping and wrapping.