Well I've only heard the phrase before in the "Happy, Happy, Joy, Joy!" song from Ren and Stimpy.
But, and this is a long shot, according to me late granny, in the Ukraine they would create Easter eggs of incredible craftsmanship and geometric complexity (I've seen photos and wooden replicas, they're quite nice). Gorgeous stuff, took hours to complete. The more impressive ones were not really eggs, just the shells and they were used decoratively.
I suppose this came from artisans growing tired of people smashing and eating their masterworks or letting them get rotten.
To make these hollow shells you has to take an uncooked, use a sewing needle to pierce a hole at the top and bottom then suck on one of the holes to get the yolk and white flowing, after which you could let the egg drain off by itself.
I've never heard the expression used like that but I do know that my Ukrainian grandmother knew something about sucking eggs.