First of all, wash the potatoes, peel them and cut them into rather small cubes (this will speed up the cooking time).

Prepare a mixture of onion, celery and carrot and brown it in a saucepan with oil.
Add the potatoes, brown them for a few minutes, then cover them with water and simmer for 20-25 minutes, until the potatoes are almost completely cooked.

Then drop the pasta into the saucepan and cook, adding more water if needed (keep in mind that the final result must not be too fluid): when the pasta is al dente and the broth has dried, turn off, season with salt and stir in smoked cheese and parmesan.

Pour into a not too large baking tray (a layer of dough about 3 cm high must come), level the surface and let it cool completely, then, with an 8 cm pastry cutter, make some molds (recompact the leftover dough to create other molds, in so as not to waste it).

Prepare a batter with frina, salt, pepper and water, mixing well so as not to create lumps.

At this point pass the omelettes in the batter, one at a time, covering them entirely, then fry them in hot seed oil, making them brown evenly.

The pasta and potato omelettes are ready: drain them on kitchen paper and serve immediately.