Preheat the oven to 400 degrees F. Soak the anchovies in a bowl of water, 5 minutes. Drain and pat dry, then finely chop and mash to form a paste; set aside.
Make the croutons: Combine the butter with the garlic in a small saucepan over medium-low heat; cook, swirling the pan occasionally, 5 minutes. Remove from the heat and pour into a medium bowl. Add the bread cubes and parsley and toss; season with salt and pepper. Arrange the bread on a baking sheet in a single layer and bake until golden brown and crisp, about 10 minutes; let cool.
Meanwhile, make the dressing: Bring a small saucepan of water to a boil. Gently lower the egg into the water, then immediately remove the pan from the heat and let stand 5 minutes. Drain and rinse the egg under cold water; crack into a large bowl. Whisk in the anchovy paste, the vinegar, Worcestershire sauce, lemon juice and mustard powder until smooth. Whisk in the olive oil in a slow, steady stream until emulsified; season with salt and pepper.
Add the lettuce, croutons and about one-third of the Parmesan to the bowl with the dressing and gently toss. Divide among plates and top with the remaining Parmesan.
Photograph by Johnny Miller
Recipe courtesy Food Network Magazine