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, stir in 1 teaspoon vinegar food coloring. NOTE: For natural dye, 10-20 drops will yield pastel colored eggs. It takes approximately half of one bottle for a deeper color tone. You can start small and add more coloring if they're not your desired shade. Artificial dye tends to have a more concentrated color versus natural dye varieties, so you'll need to use less.
Place 4 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, and soak an additional 20-30 minutes.
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. Taste and adjust the flavor and texture as desired.
Place the egg whites on a serving tray. Fill a pastry bag with a piping tip or ziploc bag with the deviled egg filling and pipe into the egg whites. You can also do this using a spoon or scoop. Refrigerate until ready to serve.