In a bowl, whisk together mayo, Parmesan, lemon juice, Dijon, garlic, Worcestershire, and anchovies (if using) until creamy. Season with salt and pepper, and thin with a splash of water to reach your desired consistency. Set aside.
Heat your Blackstone to medium (around 350–375°F). Lightly oil the surface—or use a bit of olive oil—to prevent sticking.
Lay bacon strips directly on the griddle and cook until golden and crispy, flipping as needed. Transfer to a paper towel-lined plate and set aside. Once cooled slightly, chop or crumble into bite-sized pieces.
Toss the sliced chicken with olive oil, garlic powder, onion powder, Italian seasoning, salt, pepper, and lemon juice. Spread the chicken across the griddle in an even layer. Cook 3–4 minutes per side until golden and cooked through.
Slide the tortillas onto a cooler part of the griddle for 30 seconds per side—just enough to get them pliable and slightly toasted.
In a large bowl, toss the chopped romaine with a few spoonfuls of Caesar dressing. Add the cooked chicken, crispy bacon, and extra Parmesan, mixing gently. Lay out each tortilla, spoon on ¼ of the mixture, and if desired, sprinkle with croutons for texture.
Fold in the sides of the tortilla and roll it tightly. Slice it in half, if you like, and serve immediately while everything is warm and fresh.