Preheat the oven to 350°. Bring a small saucepan of water to a boil. Add the egg and cook for 5 minutes, until soft-boiled. Remove the egg with a slotted spoon and crack it into a blender, using a small spoon to scoop out all of the egg yolk and white. Add the anchovies, lemon juice, whole garlic clove and mustard and blend until smooth. With the machine on, add 1/4 cup plus 2 tablespoons of the olive oil in a thin stream. Add two thirds of the finely grated Parmesan and season with salt and pepper.