Thoroughly wash and dry the romaine lettuce leaves. Tear into bite-size pieces and refrigerate while preparing the dressing.
In a large wooden bowl, mash the minced garlic and chopped anchovies together using the back of a wooden spoon until they form a smooth paste.
Add the room-temperature egg yolk to the garlic-anchovy paste and whisk vigorously to combine.
Whisk in the lemon juice and Dijon mustard until well incorporated.
Very slowly drizzle in the olive oil while continuously whisking to create a proper emulsion. Start drop by drop until the mixture begins to thicken, then continue with a thin stream.
Stir in the grated parmesan cheese and season with salt and freshly ground black pepper to taste.
Place the chilled romaine in a large serving bowl and toss with about two-thirds of the dressing until evenly coated.
Add the croutons and gently toss once more to distribute them evenly.
Serve immediately on chilled plates with additional dressing, freshly grated parmesan, and a twist of black pepper if desired.
