While the water is boiling, break the fide apart in your hands so that it is broken into little pieces. When the water has come to a boil, add the salt and the fide to it. Reduce heat to medium and cook, stirring occasionally for 10 minutes.
Add the olive oil to the pot, stir the fide, and cook for an additional 5 minutes.
Serve the fide soup with grated mizithra on the side.