The Christian egg-related custom is different: ahead of Easter, the yolk and white are extracted and the emptied shells are decorated. But might these egg-related customs have a common source?
This turns out to be a difficult question to answer, as we are not sure of the origin of either custom. A good place to start, then, would be the earliest-known references to them.
Mourning the lost sacrifice?
Several sources say the earliest reference to actually eating eggs at the seder is in commentary written by Rabbi Moses Isserles (1520-1572) on the code of Jewish law called "Shulchan Aruch": “In some places it is the custom to eat as part of the meal, eggs.”