Add the Greek yogurt, Parmesan, lemon juice, anchovy fillets, garlic, Dijon mustard, Worcestershire sauce, black pepper, and salt to a blender container.
Blend until the anchovies and garlic are completely incorporated and the mixture is smooth.
With the blender running on low, slowly add the olive oil until the dressing becomes creamy and emulsified.
Add the cold water and blend briefly to create a thick but pourable consistency that will evenly coat salad leaves.
Refrigerate the dressing for at least 30 minutes before serving so the garlic, Parmesan, lemon, and anchovy flavors have time to blend.