I've seen that before, but I can't remember exactly what it is...maybe an Echeveria or an Aeonium? Does it have a long 'trunk' or does it grow close to the ground?
Don't know about the edibility, though. sorry...but it if it is Echeveria or Aeonium, it is in Crassula family which include 'jade plant'.
To clarify my experience: I've been an amateur plant hobbyist for a long time, but I don't have any degrees in the area, so someone w/more relevant experience could probably give you a more exact answer...but I would guess Echeveria or Aeonium genus.