Cook the chicken: Pat chicken dry. Rub with olive oil, salt, pepper, garlic powder, and smoked paprika.
Grill over medium-high heat 5–7 minutes per side (to 165°F), or pan-sear, or air-fry at 380°F for 12–14 minutes, flipping once. Rest 5 minutes, then slice or chop.
Make the dressing (if using): Whisk Greek yogurt, mayo, parmesan, lemon, Dijon, garlic, and anchovy until smooth. Thin with water to a pourable consistency.
Season to taste.
Prep the greens: Wash and dry romaine thoroughly. Cold, dry leaves keep the wrap crisp and prevent sogginess.
Warm the tortillas: Heat each tortilla in a dry skillet 15–20 seconds per side or microwave under a damp paper towel for 10–15 seconds. Warm wraps are more flexible and less likely to tear.
Assemble: Lay out tortillas.
Spread 1–2 tablespoons dressing in the center of each. Add a generous handful of romaine, sliced chicken, a sprinkle of parmesan, cherry tomatoes, and a small handful of crushed croutons.
Wrap it tight: Fold the sides in, then roll from the bottom up, keeping tension as you roll. If needed, secure with a toothpick or wrap in foil for travel.
Finish and serve: Slice in half on the diagonal.
Add a little extra drizzle of dressing or a squeeze of lemon over the cut side for a bright finish.