Place eggs in a pot with enough water to cover them. Bring to a boil and cover.
Once water comes to a boil, reduce heat to low and cook for 2 minutes.
Remove from heat, and allow the eggs to cool in the water for 10 minutes.
Run under cold water until they are cool enough to handle. Peel eggs and rinse any shell residue.
Carefully slice eggs in half lengthwise. Place the yolks in a separate bowl and place the yolks in a bowl of warm water colored with green food coloring. *The darker the green water is, the greener your eggs will be.
Allow egg yolks to soak for 10-15 minutes, until desired color is achieved.
Combine egg yolks with the mayonnaise, relish and mustard until smooth.
Slowly add a little orange food coloring into yolk mixture until you get a soft pinkish orange color.
Place yolk mixture into a zip lock bag or piping bag and snip a small hole in the corner. *To make filling the bag easier, place it in a cup and fold the edges down over the rim.
In gentle short line motions, fill your green eggs with the yolk mixture.
Serve and enjoy your Brrraaaiiiinnnnsssss.
Refrigerate leftovers in an airtight container.