Bring a small saucepan of water to a boil. Crack the eggs into the water and cook for 30 seconds. Drain.
Combine the anchovies, garlic, salt, and pepper in a small bowl and mash to a paste with a fork. Break the egg into the mixture and whisk to blend. Add the cheese, lemon juice, and mustard and whisk well. Add the olive oil in a steady stream, whisking constantly to form a thick emulsion. Add the Worcestershire and pepper sauces and whisk well to combine. Cover tightly and refrigerate until ready to use. (The dressing will keep refrigerated for up to 1 day.)