Prepare the Eggs:

1. Boil the Eggs: Place the eggs in a saucepan and cover them with water. Bring the water to a boil over medium-high heat, then lower the heat and let the eggs simmer for about 10-12 minutes for hard-boiled eggs. Afterward, remove the eggs from the hot water and place them in a bowl of ice-cold water to stop the cooking process. Let them sit for about 5 minutes to cool down.
2. Peel the Eggs: Once the eggs are cool, peel off the shells and set the eggs aside.

Prepare the Beetroot for Coloring:

3. Make the Beetroot Infusion: While the eggs are cooling, peel and boil the beetroot in a small pot with water for about 15-20 minutes, until the beetroot is tender. Once cooked, drain the water and allow the beetroot to cool before grating it or extracting the juice. For a quicker method, you can use store-bought beetroot juice.
4. Infuse the Eggs: Cut the hard-boiled eggs in half lengthwise, removing the yolks into a bowl. Now, take a small amount of beetroot juice and drizzle it over the egg whites. Use a spoon or a small pastry brush to gently apply the juice, ensuring a pink hue without soaking the eggs. Let them sit for a few minutes to absorb the color.

Make the Filling:

5. Prepare the Filling: Mash the yolks in a mixing bowl using a fork until they are smooth. Add the mayonnaise, Dijon mustard, white vinegar (or lemon juice), and sweet pickle relish (if using). Mix everything together until smooth and creamy. Season with salt and pepper to taste.
6. Adjust the Color: If you want a more vibrant pink color, you can add a bit more beetroot juice to the yolk mixture and stir until the desired shade is reached. Be sure to taste the filling as you go to make sure it’s seasoned perfectly.

Assemble the Pink Deviled Eggs:

7. Fill the Egg Whites: Using a spoon or a piping bag, carefully fill each hollowed-out egg white with the beetroot-infused yolk mixture. You can fill them generously for a nice presentation.
8. Garnish: Sprinkle a pinch of freshly chopped parsley or chives on top for a burst of green color and freshness. Optionally, you can add a touch of paprika or even a small slice of pickled beetroot for extra flavor.

Serve and Enjoy:

9. Serve: Arrange the Pink Deviled Eggs on a serving platter, and they are ready to be served! These eggs are perfect for any occasion and will be sure to wow your guests with their vibrant color and creamy filling.