Prepare Hard-Boiled Eggs: Place eggs in a pot and cover completely with cold water. Bring the water to a full boil over high heat. Once boiling, remove the pot from heat, cover, and let the eggs stand in the hot water for 8 minutes. Drain the hot water and transfer eggs to an ice bath or run under cold water until cool enough to handle. Peel the eggs and set aside.

Prepare Beet Brine: If using fresh beets: Place the sliced fresh beets in a pot. Add 1 ½ cups water, ensuring the beets are fully submerged. Bring to a full boil, then reduce heat and simmer for 12 minutes, or until the beets are soft. If using canned beets: Drain the canned beets, reserving the beet juice. In a pot, combine the reserved beet juice with 1 ½ cups water. Add the drained canned beets to the pot if desired, for inclusion in the jar.

To the pot (containing either cooked fresh beets or the canned beet mixture), add the white vinegar, granulated sugar, and ground cinnamon (if using). Bring the mixture to a boil again, then immediately remove from heat.

Assemble and Pickle: Place the peeled hard-boiled eggs into the clean glass jar. Add the cooked fresh beet slices or drained canned beets (if using) to the jar with the eggs. Carefully pour the hot beet brine over the eggs and beets, ensuring they are fully submerged. Cover the jar tightly. Let the jar cool at room temperature for approximately 4 hours before transferring it to the refrigerator.