You'll start with hard boiled eggs. I have posts linked with tips to cook hard-boiled eggs. Boil or steam for 12 minutes, place them in an ice water bath 12 minutes, then peel.
Cut eggs in half and take out yolks and place them in a medium bowl.
Use a pastry cutter or fork to break up yolk until it's super fine.
Mix mayonnaise with mustard, s&p, and whip up with a spatula until smooth and creamy, or use an immersion blender to whip the filling.
Place mixture into a piping bag fitted with a 2D tip.
Mix 1 cup hot water, 1 teaspoon gel food coloring, and 1 tablespoon vinegar. The vinegar helps the color stay bright. I tried it both ways, and the eggs with vinegar have a brighter color.
Place egg whites into the colored water and let sit until the desired color is achieved about 1-2 minutes. Leaves some of them white if you'd to.
Take out the colored egg whites and place them on a paper towel to allow the excess color to drip off.
Then arrange eggs on a platter. Pipe the egg yolk mixture into the egg white halves.