Combine lemon juice, anchovy, garlic, and mustard in a blender and puree until smooth (if using hand blender, use narrow container only). Slowly add oil, drop by drop, to make a creamy dressing. Transfer to a bowl and stir in ¼ cup of the Parmesan cheese. Season with salt and pepper to taste. Cover and chill. May be done several days in advance.
Separate egg white from yolk. Place cooked egg white in a coarse mesh strainer and press through with a spoon (or run over grater) collecting in a bowl. Repeat with cooked egg yolk, using a clean strainer and collect in a separate bowl.
Prepare the kale: peel stalks, cut leaves away from center stalks and then thinly slice crosswise. Toss kale and dressing in a large bowl to coat. Season with salt (if necessary) and pepper. Top with remaining 1/4 cup Parmesan cheese and sieved eggs.