Boil water, salt, sugar and vinegar. Add the grated beets and simmer for 30 minutes. Let cool and strain the beets.
Boil 4 eggs until they are hard boiled. Let them cool.
Peel the eggs and make sure that there is no piece of shell remained. Add the peeled eggs in the beetroot vinegar and let it rest overnight. These eggs can be marinated, chilled, in an airtight container up to 3 days.
Half the eggs and top/fill them with your favorite filling.