Use regular supports to support the base of the egg or slice a little bit off the bottom for the same effect.
Split the model to its pieces and use fuzzy skin on of them to change the texture of this part if you want (you can also change its color if you have an MMU). I used 3mm distance and 1mm thickness but you can adjust these values to your liking.
You can also print only one part alone and have a spring/screw in an egg shape
The multi texture effect was inspired by this video: