Place the eggs in a pot and cover them with cold water. Bring to a boil over medium-high heat. Once boiling, cover the pot and remove it from the heat. Let it sit for 10 minutes.
After 10 minutes, carefully drain the hot water and transfer the eggs to an ice bath. Let them cool for about 5 minutes.
Once cool, gently tap each egg on a hard surface and peel under running water to make peeling easier.
Cut each egg in half lengthwise and carefully remove the yolks into a mixing bowl. Place the egg whites on a serving platter.
Mash the yolks with a fork and mix in the mayonnaise, Dijon mustard, vinegar, salt, and pepper until smooth and creamy.
To color the egg whites, mix food coloring with water in small bowls. Dip each egg white half into the dye for a few seconds until you achieve the desired shade. Use tongs or a spoon for easy handling.
Once dyed, place the colored egg white halves on paper towels to dry slightly.
Spoon or pipe the yolk mixture back into the colorful egg whites.
Serve immediately or refrigerate until ready to serve.