Prepare the Creamy Caesar Dressing: In a medium bowl, whisk together the mayonnaise, 1/4 cup grated Parmesan, fresh lemon juice, Dijon mustard, Worcestershire sauce, minced garlic, and anchovy paste (if using). Season generously with freshly cracked black pepper. Taste and adjust seasoning if necessary. Set aside.
Cook the Chicken: Pat the chicken breasts dry and season both sides with salt, pepper, and garlic powder. Heat the olive oil in a large skillet over medium-high heat. Cook the chicken for 6-8 minutes per side, or until golden brown and the internal temperature reaches 165°F (74°C). Transfer to a cutting board and let rest for 5 minutes before dicing.
Prep the Salad Components: In a large bowl, combine the chopped romaine lettuce, diced chicken, 1/2 cup shaved Parmesan, and crushed croutons (if using). Add a few spoonfuls of the Caesar dressing, just enough to lightly coat the ingredients, and toss gently to combine.
Assemble the Perfect Wrap: Warm the tortillas in a dry skillet or microwave for 15-20 seconds to make them pliable. Lay a warm tortilla on a flat surface. Spoon a quarter of the chicken and lettuce mixture onto the center, leaving a 2-3 inch border. Fold in the left and right sides, then tightly roll the wrap from the bottom up, tucking in the filling as you go.
Slice and Serve: Use a sharp serrated knife to slice the wrap in half on a diagonal. Serve immediately or wrap in foil for a later meal.