Cook the eggs until hard-boiled, cool them completely, and peel away the shells. Keep the egg whites as smooth as possible so the beet color can develop evenly.

Drain the liquid from the canned beets into a small saucepan and reserve the beet slices. The dark beet juice will become the foundation of the pickling brine.

Add the white vinegar, cider vinegar, sugar, and salt to the saucepan. Stir until the sugar and salt begin to disappear into the red liquid.

Bring the brine to a boil, then let it simmer for 5 minutes. The finished brine should smell sweet, sharp, and earthy with no visible sugar granules.

Arrange the peeled eggs in a clean glass jar and place the reserved beet slices over them. Leave enough room for the brine to surround every egg.

Let the brine cool slightly, then pour it over the eggs and beets until everything is submerged. Warm brine is gentler on the egg whites than steaming-hot liquid and helps prevent a rubbery exterior.

Cover the jar and refrigerate it for at least 2 days before serving. The egg whites will begin developing a pale pink edge as the beet brine works inward.