Halve the boiled eggs, remove the yolks, and place the yolks in a separate bowl. Cover and refrigerate the yolks while dying the egg whites.
Fill three 2-cup size bowls with 1 1/2 cups water each. To each bowl, add 1 teaspoon vinegar. Depending on the amount of color you want for the egg whites, add 10-20 drops of natural food coloring. (Artificial dye/food coloring is more concentrated in color versus natural dye varieties, so less than 5-10 drops should be sufficient.) Stir until well combined.
Place 6 egg whites in each bowl. Let the egg whites soak in the colored water for 20-30 minutes, or until they reach your desired color intensity. Add more drops if they’re not at your desired color.
Once colored, remove the egg whites from the colored water, and gently pat dry with paper towels.
Mash the egg yolks with a fork until smooth. Add mayonnaise, dijon mustard, salt, and white pepper. Mix until well combined and creamy.
Place the egg whites on a serving tray. Spoon or pipe the egg yolk mixture into the egg whites.