Wash the romaine heads thoroughly, then dry them completely using a salad spinner or clean kitchen towel. This step matters more than people think, since wet leaves water down the dressing. Chop the romaine into bite-sized pieces and set it aside in your largest bowl.
In a small bowl, combine the mayonnaise, minced garlic, Parmesan, lemon juice, Dijon mustard, Worcestershire sauce, and anchovy if using. Whisk everything together until it looks smooth and creamy. Slowly drizzle in the olive oil while whisking so the dressing comes together evenly.
Give the dressing a taste before you commit it to the whole salad. Add salt and pepper gradually, keeping in mind the Parmesan already brings some saltiness. Adjust the lemon juice too if you want extra brightness.
If you're using rotisserie chicken, remove the skin and shred or slice the meat into bite-sized pieces. If cooking your own, season chicken breasts with salt and pepper, then pan-sear or grill until fully cooked through, about 6 to 7 minutes per side.
Add the chicken, croutons, and most of the Parmesan to the bowl of romaine. Pour the dressing over everything a little at a time, tossing gently so every leaf gets coated without turning mushy.
Sprinkle the remaining Parmesan over the top and add a few extra croutons for crunch. Serve immediately while the romaine is still crisp and the chicken is fresh.