Mince the garlic clove finely. If using anchovy fillets, mince them very finely as well. Use the side of a chef's knife to mash them into a paste so they integrate smoothly into the dressing.

Combine base ingredients

In a medium bowl, add the mayonnaise (or prepared egg-yolk emulsion), Dijon mustard, Worcestershire sauce, and lemon juice. Whisk until smooth and slightly thinned.

Incorporate garlic and anchovy

Add the minced garlic and anchovy paste to the bowl and whisk until fully incorporated, so the dressing has an even savory flavor.

Add cheeses and oil

Whisk in the grated Parmigiano Reggiano and the finely grated Parmesan. Slowly drizzle in the olive oil while whisking to create a slightly glossy, cohesive dressing.

Season

Taste and season with kosher salt and freshly ground black pepper. Adjust lemon for acidity, salt or pepper to taste. The dressing should be bright, savory, and slightly tangy.

Salad

Prepare lettuce

Make sure romaine pieces are dry — spin in a salad spinner or pat with paper towels. Excess water will dilute the dressing.

Toss lettuce with dressing

Place the romaine in a large bowl. Add about half of the dressing and toss gently to coat. Add more dressing a little at a time until leaves are evenly coated but not dripping (approximately 2–3 tablespoons dressing).

Add croutons and cheese

Add the croutons and gently fold them into the dressed lettuce so they start to absorb some dressing. Sprinkle the Parmigiano Reggiano shavings over the salad.

Finish and serve

Finish with a light dusting of freshly ground black pepper (about 1/4 tsp). Taste and add a small pinch of salt if necessary. Serve immediately so croutons remain crisp.