Remove outer leaves if wilted. Cut romaine heads lengthwise, then slice crosswise into 1–1.5 inch ribbons. Rinse in cold water, spin dry in a salad spinner or pat dry thoroughly with clean kitchen towels. Dry leaves so dressing adheres.

Shave Parmesan

Reserve 3 tablespoons of the grated Parmesan for the dressing. Using a vegetable peeler or knife, shave additional Parmesan into thin curls (about 1/2 cup) for topping the salad.

Assemble

Place the dried romaine in a large salad bowl. Add croutons and the Parmesan curls but wait to add dressing until after dressing is made.

Dressing

Prepare anchovies and garlic

Mince the garlic finely. Finely chop or mash the anchovy fillets with the flat of a knife on a cutting board until they form a paste (this mellows their flavor and distributes it through the dressing).

Emulsify dressing

In a medium bowl, whisk together the mayonnaise, Dijon mustard, Worcestershire sauce, minced garlic and anchovy paste, reserved 3 tablespoons grated Parmesan, and fresh lemon juice. While whisking continuously, drizzle in the olive oil slowly to create an emulsion (thick, glossy dressing).

Season dressing

Taste and season with salt and black pepper. If too thick, whisk in up to 1 teaspoon of water or extra lemon juice to reach desired consistency.

Dress salad

Add 3–4 tablespoons of dressing to the salad bowl and toss gently but thoroughly to coat the leaves. Add more dressing a tablespoon at a time until leaves are coated to your liking (typically 4–6 tablespoons total for 2 heads of romaine).

Finish and serve

Divide dressed salad among plates or serve family-style. Top with shaved Parmesan curls and an additional grind of black pepper. Optionally serve with lemon wedges and extra anchovy fillets on the side.