In a medium bowl, toss the bread cubes with 3 tablespoons olive oil, the garlic powder, 1/4 teaspoon salt, and 2 tablespoons Parmesan until every cube looks glossy.

Spread the cubes in a single layer on the pan and bake for 12 to 15 minutes, stirring once at 7 minutes, until deep golden and hollow when tapped.

While the croutons bake, mash the minced anchovies and grated garlic with a fork in a medium bowl until they form a smooth, pale paste.

Whisk in the mayonnaise, 2 tablespoons olive oil, lemon juice, Dijon, and Worcestershire until creamy with no streaks of mustard.

Stir in 1/3 cup Parmesan, the pepper, and 1/8 teaspoon salt. Add cold water 1 teaspoon at a time until the dressing falls from the whisk in a thick ribbon.

Cool the croutons on the pan for 10 minutes while the dressing chills in the fridge, until a cooled cube snaps cleanly.

Toss the romaine with about two thirds of the dressing for 30 seconds until every leaf looks lightly glossy, then add more to taste.

Add the croutons and shaved Parmesan, toss 3 or 4 times, and serve right away with black pepper and lemon wedges.