Make the shawarma chicken: In a large bowl combine the Greek yogurt, olive oil, chopped garlic, chopped shallots, smoked paprika, dried oregano, turmeric, chili flakes (to taste), and salt; add the sliced chicken and toss to coat. Let marinate 15 minutes if you have time.
Preheat the oven to 425°F (220°C). Arrange the marinated chicken in a single layer on a baking sheet and bake for about 20 minutes, or until cooked through.
Switch the oven to broil and broil the chicken 1–2 minutes until the edges char slightly; watch closely to avoid burning.
Assemble the sandwiches: Lay each piece of naan flat on a baking sheet and spread about 1–2 tablespoons of Caesar dressing, mayo, or garlic tahini over one side of each naan.
Top the dressed naan with sun-dried tomatoes, sliced pickles and/or pepperoncini, a layer of Havarti and gouda slices, and divided cooked chicken. Cover the filled naan with foil and bake for 15 minutes, until the cheese is melted.
Remove the foil, top each sandwich with fresh sprouts and pickled red onions if using, drizzle more dressing or tahini, fold the naan over the fillings, then brush the top with a little oil and sprinkle with sesame seeds if desired.
Return to the oven and bake another 5 minutes until the naan is toasted. Slice and serve warm with extra dressing on the side.
