Place eggs in a pot and cover with water; bring to a boil for 10 minutes. Transfer eggs to a colander and run under cold water until completely cooled. Peel eggs, cut in half lengthwise, and scoop egg yolks into a small bowl. Place egg whites onto a serving plate.
Mash egg yolks with a fork until crumbly. Stir mayonnaise and mustard into yolks until smooth. Fold spinach into mayonnaise mixture; season with salt and pepper. Spoon mixture onto the egg whites; top each egg with Parmesan cheese. Refrigerate until completely chilled, at least 1 hour.