Pat chicken dry, coat with olive oil, and season both sides with garlic powder, salt, and pepper. Heat a large skillet or grill pan over medium-high heat. Cook chicken for 6–7 minutes per side until golden brown and internal temp reaches 165°F. Transfer to a cutting board, rest 5 minutes, then slice thinly against the grain.

In a medium bowl, whisk together mayonnaise, grated Parmesan, anchovy paste, lemon juice, Dijon, minced garlic, and a pinch of salt. Stream in cold water while whisking until smooth and pourable. Taste and adjust salt, lemon, or anchovy as desired. Set aside.

In a large bowl, combine chopped romaine, half the shaved Parmesan, crushed croutons, and ¼ cup of the dressing. Toss well to coat evenly. Add more dressing if needed—it should be creamy but not soggy.

Wipe the skillet clean and warm each tortilla over medium heat for 20–30 seconds per side until pliable and lightly blistered. Stack them on a plate and cover with a clean towel to keep warm.

Place a warm tortilla on a flat surface. Spread 1 tablespoon of dressing in a horizontal line down the center (this acts as glue). Pile ¼ of the dressed romaine mixture, top with a quarter of the sliced chicken, and sprinkle with remaining shaved Parmesan. Fold in the sides, then roll tightly from the bottom up, pressing gently.

For a crispy finish, return the rolled wraps to the skillet, seam-side down, over medium heat. Cook for 1–2 minutes per side until golden and the seam is sealed. Use a sharp serrated knife to cut each wrap in half diagonally. Serve immediately with extra dressing.