Combine all the liquid from canned or jarred beets (reserving the beets), apple cider vinegar, sugar, pickling spice, and black peppercorns to a medium saucepan. Bring to a slow simmer for 5 minutes, allowing all ingredients to combine. Remove from heat and allow to cool.
Once beet liquid mixture is cool enough to touch add reserved sliced beets (I typically only use half of the beets and reserve the other half for a salad or other use), sliced onion, and peeled hard-boiled eggs.
Transfer entire mixture to a large container (a mason jar or large glass bowl will do) and refrigerate for at least 24 hours or up to 7 days.
Slice eggs and remove yolk. Combine yolk, mayonnaise, butter, salt and pepper in the bowl of a food processor. Pulse until well combined and fluffy.
Fill egg halves with yolk mixture and top with sliced chives. Optional, you can also garnish with the pickled onions from the mixture.
To use fresh beets: Scrub 1lb fresh red beets, add to a pot and cover with water. Boil until tender, about 30-50 minutes (depending on size of beets). Remove beets from water and when cool enough to handle slice and reserve. Continue with recipe, do not throw away the beet cooking liquid, this will be your base for the pickled eggs.