Fry the potato slices in the olive oil until they get golden-colored and slightly crisp. Reserve them dry apart.
Using some of the already used oil, fry slowly the onion bits in a wide pot. Whenever the onion gets semitransparent, put the stock in and keep heating for 2 minutes.
Then, put the slices carefully inside the pot. Add the salt as desired. Keep heating till water level equals potato level, 20 minutes approximately.
Crack the eggs over the surface of the potatoes and the branch of parsley. Let the eggs harden for at least 5 minutes.
TIPS: Serve hot enough. An egg per person should be polite.