Well judging from the picture you posted i can tell you the easy out broke because you are about 75% in the bolt and about 25% in the housing so when you turned it you kinda made a lock nut thus snapping your easy out. Two best things i can tell you is bring it to a machine shop and have them extract the broken bolt witch shouldn't be a problem at all.2nd you could try and weld a nut on top so you could remove it with a socket but i would say the machine shop would be your best option at this point.