First prepare the filling. Peel and cube the potatoes and cook in boiling, salted water until tender - about 15-20 minutes. Drain and return to the heat for a few minutes to evaporate some more of the liquid.
Rice the potatoes with a potato ricer or pass them through a fine sieve.
Add the remaining ingredients and stir well. Set aside for an hour, at room temperature, to cool.
To prepare the pasta dough whisk together the flour and semolina until combined. Add the olive oil and sea salt and add about 100 ml of the lukewarm water, adding a tablespoon at a time of the remaining water until a dough forms.
Knead for two minutes until smooth and elastic, adding a little bit more water at a time if needed. I just dipped my fingers into the water to add it to the dough.
Cover in cling film and leave for half an hour.
Cut the dough into two equal portions and run each half through a pasta machine, starting with the thickest setting. Fold the dough into thirds and run through the thickest setting again. Repeat, if needed, to get an even width of pasta. Run the dough through the machine again a few more times, selecting a thinner setting for each run. I rolled mine until it was at the second thinnest setting.
Using an 8 cm round cutter (I used a glass tumbler) cut the dough into circles and place on a floured surface.
Place a heaped teaspoonful of the potato filling into the centre of each pasta round.
Cup the round in the palm of your hand like a taco shape. Pinch about 1 cm of the end together. Push the pinched dough in and slightly to the left, folding the edge of the dough into a bend and pinch that in and slightly over. Repeat on the other side. (Watch the video link above to see how to do this).
Continue pinching and folding the dough over and down all the way up to the top of the dough and pinch the end closed. You will have a filled pocket resembling a wheat sheaf. Set aside on a floured surface and repeat with the remaining circles.
Bring a large pan of salted water to the boil and boil the culurgiones in batches for five minutes.
Meanwhile, prepare the sauce. Heat the oil in a saucepan and gently fry the garlic for a minute or so until its aroma is released. Add the passata and cook for three minutes.
Remove the sauce from the heat and stir in the torn basil.
Serve the culurgiones immediately with a little bit of the sauce with extra basil and grated Pecorino cheese.
Leftover culurgiones can be frozen for later. Simply cook from frozen.
There are regional variations of this dish. Some add gently fried onions to the filling. Others use fresh tomatoes in the sauce, in which case cook them for 8-10 minutes only.