To coddle the eggs, bring a small pot of water to a boil. Carefully lower the eggs into the water, and cook 1 minute. Use a slotted spoon to transfer the eggs to a bowl of ice water. When the eggs are cool, separate them, setting aside the yolks for the dressing. (Use the whites for baking, an egg-white omelet, a Pisco Sour cocktail, etc.)
In a large bowl (ideally wooden, like they do at Caesar’s Restaurante & Bar!), combine the mustard, Worcestershire sauce, anchovies, lemon juice, garlic, and cheese and pepper. Beat with a wooden spoon until a paste forms. Then beat in the coddled egg yolks. Add the oil in a thin stream, beating constantly until it’s incorporated.
Use immediately or refrigerate up to 3 days. (Makes about 1 cup.)