It's not, technically, "egg-shaped". It's an extremely oblate spheroid - a sphere that's been "squashed" at the poles. It's caused by the planet in question rapidly rotating.A true "egg-shape" would be made by stretching the poles, not squashing them.
Gas giants are commonly found with such oblateness, as they usually rotate quite rapidly and a ball of gas is much more easily deformed than a ball of rock and metal. But oblate solid worlds are not unknown. They are, almost always, a moon that is orbiting in very close proximity to its parent body. Here's a highly oblate moon I found some time ago:
In theory, true egg-shaped worlds should exist in the real-world universe - a tidally-locked object in close proximity to its parent ought to be extremely deformed at the "inner pole" and "outer pole". But such tidal deformation is not currently modelled in ED, so actual "space eggs" ought to be impossible.