Summary

I didn't like any of the other available designs, so here's my egg case composed of two parts that screw together. The inner chamber is an ellipsoid with a diameter of 49mm and height of 62mm, which empirically works for EU size L eggs (the dimensions aren't standardized – only weights are – so yours might differ). If you prefer larger eggs, scale the print accordingly.
The design features a textured surface for easy grip and vent holes, which are VERY important as I discovered with one of my previous designs – residual moisture can make the egg case stink quickly, and it needs to evaporate somehow. The end vents are also helpful when trying to take a ˢᵐᵃˡˡ egg out – you can just push it out with your finger. The textured grip and vent holes follow a spiral phyllotaxis pattern on the surface of the outer ellipsoid, generally vibe-coded from the ideas found at https://blog.wolfram.com/2011/07/28/how-i-made-wine-glasses-from-sunflowers/.
It prints fine with any dirt-cheap PLA, ideally with the poles (ends) facing down (no supports needed then), a brim, and 15% gyroid infill.
Vibe coded with Claude in PythonSCAD, https://pythonscad.org/.