Place the finely minced anchovy fillets and the minced/grated garlic on a cutting board. Sprinkle a tiny pinch of salt and use the flat side of a chef's knife to press and scrape repeatedly to form a smooth paste (about 30–45 seconds). This mellows the anchovy and blends it into the dressing.

Emulsify base

In a medium bowl, combine the mayonnaise, Dijon mustard, Worcestershire sauce, and lemon juice. Whisk until smooth.

Add oils and seasonings

Whisk in the olive oil gradually in a steady stream until the dressing is glossy and slightly thickened. Stir in the anchovy-garlic paste, grated Parmesan, 1/4 tsp freshly ground black pepper, and 1/4 tsp salt. Taste and adjust acidity (add up to 1 tsp more lemon juice) or salt as needed.

Rest

Cover and refrigerate the dressing for at least 15 minutes to allow flavors to meld. If making ahead, refrigerate up to 48 hours; whisk again before using.

Salad

Prepare lettuce

Remove any wilted outer leaves from the romaine heads. Cut off the root end, halve each head lengthwise, then slice crosswise into roughly 1-inch wide ribbons, or tear into bite-sized pieces. Rinse under cold water and spin dry in a salad spinner or pat thoroughly with clean kitchen towels to remove excess water.

Season lettuce

Place the dried romaine in a large mixing bowl. Sprinkle 1/2 tsp salt and 1 tsp freshly ground black pepper over the leaves and toss briefly to distribute.

Dress the salad

Add about 3–4 tablespoons of the prepared Caesar dressing to the bowl (start with less; you can add more to taste). Toss the lettuce gently but thoroughly until leaves are evenly coated. Add more dressing in 1-tablespoon increments if you prefer a wetter salad.

Finish and serve

Add 1.5 cups croutons and 3 tablespoons freshly grated Parmesan to the dressed lettuce. Toss lightly to combine. Transfer to a serving bowl or plates and garnish with an extra sprinkle of Parmesan and a grind of black pepper. Serve immediately so croutons stay crisp.