Make the dressing: Smear the garlic paste over the inside of the salad bowl. Put the anchovies, egg yolks, mustard, lemon juice, and water into a blender and process for 30 seconds until the mixture is smooth. With the blender running, pour the olive oil in slowly for the dressing to emulsify. Stir in the Parmesan, a pinch of salt and a couple of grinds of black pepper; set aside. (Refrigerate the dressing if you will not be using it right away.)
Assemble the salad: Tear the lettuce into a large bowl. Add enough dressing to coat the salad to your liking. Add some extra Parmesan and toss the salad well. Serve immediately.