Cypriot style asparagus with eggs and potatoes (Αγρέλια με αυγά)

Αγρέλια με αυγά (asparagus with eggs) is a traditional delicacy served in taverns as a meze, but I mostly enjoy them as a light dinner dish.
This dish includes potatoes and therefore can be considered as a complete meal.
Two versions have been created today, one the traditional way and the other a little more contemporary!