Hard-boil 6 to 12 eggs
Cool the eggs in ice water
Peel the eggs
Slice or chop 1 to 2 cooked beets
In a saucepan, combine 1 cup vinegar, 1 cup water, 1 cup beet juice, 1/2 cup sugar, 1 teaspoon salt, and optional spices like peppercorns, cloves, or allspice
Bring the mixture to a boil
Stir until the sugar and salt dissolve
Remove from heat and let the brine cool slightly
Place the peeled eggs and beets in a clean jar
Pour the warm brine over the eggs and beets until fully covered
Seal the jar
Refrigerate for at least 3 days before eating
Keep refrigerated and use within 1 to 2 weeks