Make the dressing. In a bowl, whisk Greek yogurt, olive oil, lemon juice, Dijon, garlic, Worcestershire, anchovy, and Parmesan. Season with salt and pepper.
If it’s too thick, whisk in a splash of water or milk until it’s creamy and pourable.
Prep the chicken. If using rotisserie, pull the meat and chop or shred. For grilled or poached chicken, slice thinly. Toss the chicken with 2–3 tablespoons of the dressing to keep it juicy.
Prep the greens. Wash and dry romaine thoroughly so the wrap doesn’t get soggy.
Chop into bite-size pieces. Halve cherry tomatoes and slice any optional red onion or avocado.
Warm the tortillas. Heat each tortilla in a dry skillet for 15–20 seconds per side or microwave under a damp paper towel for 15–20 seconds. Warm wraps are more flexible and less likely to tear.
Assemble the salad base. In a large bowl, toss romaine with enough dressing to lightly coat. Add half the Parmesan and toss again.
Stir in crushed croutons for crunch.
Build the wraps. Lay each tortilla flat. Add a generous layer of the dressed romaine, then chicken, then tomatoes, onion, and avocado if using. Sprinkle with remaining Parmesan and a crack of black pepper.
Wrap it up. Fold the sides in, then roll tightly from the bottom up.
If needed, secure with a toothpick. For a café-style finish, sear the seam side down in a skillet for 1–2 minutes to seal and add a slight crisp.
Serve. Slice in half and serve immediately with extra dressing on the side for dipping.