Separate egg white from yolk. Place egg white in a coarse-mesh strainer set over a bowl. Press egg white through strainer with the back of a spoon; scrape egg white from bottom of strainer. Repeat with egg yolk, using a clean strainer and bowl. DO AHEAD Can be made 6 hours ahead. Cover bowls separately and chill.
Toss kale and dressing in a large bowl to coat. Season to taste with salt and pepper. Top with remaining 1/4 cup Parmesan and sieved eggs.