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.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.