Combine the water, vinegar, sugar (if using), salt, and the sliced beet together in a saucepan and bring to a boil. Place a lid on your pan and reduce the heat to maintain a steady simmer. Continue to simmer until the beet is fork tender, about 20 minutes. Turn off the heat and pour the liquid and beet into a large, heat safe bowl.
Allow your liquid to cool completely, then add the eggs and place plastic wrap on top. Carefully transfer bowl to the fridge and allow your eggs to chill for 2 hours.
Remove your eggs from the beet juice, and place on a cutting board; discard the beet and juice. Pro tip: wear gloves if you don't want pink hands! Slice the eggs in half, and place the yolks in a large bowl. Place the egg whites on a platter.
Add all other filling ingredients to a bowl with the yolks and mash with a fork until combined.
Fill the egg whites, either with a spoon or transfer the filling to a piping bag or a small baggie with the tip removed. Enjoy!
Notes
To hardboil the eggs: Cover the eggs in a large pot with 1 1/2" of water. Bring water to a boil, then cover the pot with a lid and turn off the stove. Allow your eggs to cook like this for 18 minutes. Once done, remove them using a slotted spoon to an ice bath. Peel and they're ready to use!