First, hard boil the eggs. Add eggs to a pot and fill with water, to about an inch above the eggs. Bring to a rolling boil and remove from heat. Let sit for 10-12 minutes. Strain the water and from the pot and run cold water over the eggs to cool them down. Once cooled, peel the shell off the eggs.
Cut eggs in half lengthwise and carefully scoop out the yolks into a bowl.
Add mayonnaise, mustard, salt and pepper to bowl and stir until combined.
Put 5 drops of red food coloring into a bowl of water and 5 green into another bowl of water. Place the egg whites into the colored water and allow to sit in the water for 10-15 minutes, or until the eggs are the shade you like.
Pat the colored eggs dry.
Fill the egg whites with the egg mayonnaise mixture.
Arrange on a plate, cover and refrigerate up to 24 hours.