Preheat oven to 375°F (190°C). Toss the bread cubes with 1 tablespoon olive oil and 1/4 teaspoon salt in a bowl until evenly coated. Spread in a single layer on a baking sheet. Bake 10–12 minutes, stirring once halfway through, until golden brown and crisp. Remove and let cool.

Caesar dressing

Make dressing

In a medium bowl, mash the minced anchovy fillets and minced garlic to a paste with the back of a spoon. Whisk in the mayonnaise, lemon juice, Dijon mustard, and Worcestershire sauce until smooth. Add the grated Parmesan, then slowly whisk in the 2 tablespoons extra-virgin olive oil until emulsified. Taste and season with 1/4 teaspoon salt and more lemon or salt if needed.

Salad assembly

Wash and dry the romaine lettuce well; discard any wilted outer leaves. Tear or chop the lettuce into roughly 1- to 2-inch pieces and place in a large bowl.

Add about 3/4 of the dressing to the lettuce (reserve some for serving) and toss gently with tongs until leaves are evenly coated but not drenched. Add the cooled croutons and toss once more to combine.

Transfer to a serving platter or divide into portions. Sprinkle the shaved Parmesan over the top, then dust with the freshly ground black pepper. Serve immediately with extra dressing on the side.