In a medium bowl, whisk together Greek yogurt, mayonnaise, and olive oil until smooth. Add mashed anchovy fillets, fresh lemon juice, Worcestershire sauce, Dijon mustard, and minced garlic. Season with salt and pepper to taste.

In a large mixing bowl, combine chopped rotisserie chicken, Romaine lettuce, and halved grape tomatoes. Sprinkle in finely shredded Parmesan cheese, mixing gently to incorporate all the ingredients.

Drizzle the homemade dressing over the salad mixture and gently toss using tongs or a spoon until evenly coated.

Carefully add in diced avocado, mixing gently to avoid mashing, until just incorporated.

Lay out tortillas on a clean surface. Spoon a generous amount of the salad mixture along the center of each tortilla and wrap them securely around the filling.

Cut each wrap in half diagonally for easy handling and serve immediately.