Make the sauce: In a bowl, whisk Greek yogurt, lemon juice, Dijon, Worcestershire, anchovy paste (if using), garlic, olive oil, and 2 tablespoons Parmesan. Season with salt and plenty of black pepper. Thin with a splash of water or milk until slightly pourable but still creamy.
Prep the chicken: Toss the cooked chicken with 2–3 tablespoons of the Caesar sauce to coat.
This keeps it juicy and flavorful.
Warm the flatbread: Brush flatbreads lightly with olive oil. Warm in a 400°F (200°C) oven for 3–5 minutes, or toast in a skillet until edges are just crisp.
Toss the lettuce: In a large bowl, toss romaine with enough Caesar sauce to lightly coat. You want glossy leaves, not soggy ones.
Assemble: Top warm flatbreads with dressed romaine, then add the sauced chicken.
Sprinkle with Parmesan. Add tomatoes and a few slivers of red onion if you like.
Finish: Crack fresh black pepper over the top and drizzle a little extra sauce if you want. Slice and serve right away.