Is it necessary to cook eggs in a seperate egg pot?


There is no such Halacha, rather a custom developed by some families, out of concern that the pot might become Treif (due to blood that may be found). Nowadays, with unfertilized eggs (see here), there is less reason to follow this custom.


Regarding Pesach, please see here: 

Egg Pot for Pesach

See also here: 

I want to experiment with cooking hard-boiled eggs. Can I try with cooking only one egg?