This is the last of the Hlaalu quests you get in Balmora. The mine is an ebony mine, not an egg mine. The Hlaalu woman in Balmora, whose name escapes me, says that you can either convince the imperial official in Ebonheart to buy from House Hlaalu or shut down the Redoran Sudanit ebony mine by killing the mine boss. She also says there may be a bonus if you do both. The Sudanit ebony mine is located not far south of Ghostgate.
I tried stealing some ebony to make everyone attack me and duly slaughtered every living thing in the mine but all that earned me was an enormous price on my head
