Place the eggs in a saucepan, cover them with cold water and bring to a boil. Cook for 9 minutes, then immediately run them under cold water and peel them. Cut them in half lengthwise.
Heat a non-stick pan over medium heat, without oil.
Distribute the Parmigiano in well-spaced round mounds, one for each half egg.
Place a half egg on each mound.
Cook without touching for 3-4 minutes, until the Parmigiano melts and forms a golden and crispy wafer. Flip briefly to the other side.
Remove gently and serve immediately, hot.
