If using anchovy fillets, mince them with a pinch of salt into a paste using the flat side of a chef's knife or finely chop. Mince the garlic cloves finely and lightly smash with the knife to release oils.

Combine base ingredients

In a medium bowl, whisk together the mayonnaise, Greek yogurt, lemon juice, Dijon mustard, Worcestershire sauce, and chopped capers (if using) until smooth.

Incorporate anchovy and garlic

Stir the anchovy paste (or anchovy fillets) and minced garlic into the mayo mixture until evenly distributed.

Emulsify with oil

Slowly drizzle the extra-virgin olive oil into the dressing while whisking constantly to create a smooth, slightly thick emulsion.

Season and finish

Taste and season with salt and freshly ground black pepper. Adjust lemon juice for brightness or a little more olive oil if too tangy. The dressing should be creamy and balanced—about 3/4 cup total.

Salad

Prepare romaine

Remove any wilted outer leaves from the romaine hearts. Slice each heart in half lengthwise, then crosswise into 1- to 2-inch pieces depending on preferred bite size. Rinse thoroughly under cold water and spin dry in a salad spinner or pat dry with clean towels until leaves are crisp.

Toss with dressing

Place the dried romaine pieces in a large bowl. Add about half to two-thirds of the dressing and toss gently but thoroughly to coat the leaves. Add more dressing to taste — you want an even coating but not a heavy puddle at the bottom.

Add cheese and croutons

Sprinkle 1/2 cup of the grated Parmesan over the tossed salad and add the croutons. Toss once more gently to distribute evenly.

Plate and finish

Divide the salad among serving plates or a single large platter. Sprinkle the remaining grated Parmesan and shaved Parmesan on top. Grind fresh black pepper over each portion and add lemon wedges on the side for optional brightness.

Serve

Serve immediately so the croutons remain crisp. If preparing ahead, keep dressing separate and toss just before serving to maintain texture.