Place the eggs in a saucepan, cover with water, and bring to a boil over medium-high heat. Once boiling, reduce heat to low and simmer for 10 minutes. Remove eggs and cool in ice water.
Peel the eggs carefully once cooled and slice each egg in half lengthwise. Gently remove the yolks into a mixing bowl, keeping the egg whites intact.
Mash the yolks with a fork until smooth, then stir in mayonnaise and mustard until you get a creamy filling. Season with salt and pepper to taste.
Fill a piping bag or plastic sandwich bag with the yolk mixture, snip the tip, and pipe the filling into each egg white half smoothly, creating a rounded 'eyeball' shape.
Mix a few drops of red food coloring into a small amount of water and dip the outer edge of each egg white to give the appearance of bloodshot sclera.
Use additional red food coloring to color small portions of the yolk filling to mimic the blood vessels around the 'iris'.
Cut small circles from black olives or use black olive slices to create the 'pupil' and place one in the center of each egg's yolk. For extra creepiness, add tiny olive slices as veins around the iris.
Arrange the finished eyeball deviled eggs on a platter. Chill briefly if desired, then serve to spooky delight.
