For the dressing: Place the egg yolk, mustard, anchovies, garlic, vinegar, lemon juice, and a dash of Worcestershire sauce in a blender. Blend until pureed. With the motor running, add the olive oil in a slow, steady stream until it is fully incorporated. If the dressing stops moving in the blender, stop the machine, add the warm water and then continue until all the oil is added. To finish, add the cheese and blend on low speed to incorporate. Makes about 1 1/2 cups.
For the croutons: In a large skillet over medium-high heat, melt the butter until it begins to foam. Add the chopped garlic and cook for 1 minute. Add the bread slices and mix to coat. Toss bread occasionally so that both sides get toasted. When the bread is golden brown, add the Parmesan and toss to coat. Remove from the heat and allow to cool.
For the salad: Put the whole romaine leaves in a work bowl. Add enough of the dressing to coat the leaves and toss well. Add the croutons and toss again to combine. Sprinkle the Parmesan over all and serve.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.