First boil the potatoes: put them in a large pot full of water, bring to a boil and cook for at least 30 minutes before testing the cooking with a fork.
Drain them, peel them, mash them and let them cool.
Once completely cold, take the potatoes again, add the pecorino and chopped mint, mix together and finally add salt, pepper, oil and grated garlic.
Cover with plastic wrap and let it rest in the fridge overnight or at least 8 hours.
Spend the 8 hours, recover the filling from the fridge and prepare the pasta: pour a large flour and semolina into a bowl, add water, oil and a pinch of salt and knead until the dough is smooth and homogeneous.
Cover with plastic wrap and let stand for 30 minutes at room temperature.
With a leaf-pulling machine, roll out the dough gradually from the widest thickness to the penultimate.
With a 9 cm pastry cutter made of disks. Put a teaspoon of filling in the center and gently press it to flatten it slightly.
At this point tighten the base between two fingers to close the dough, then fold a little bit of dough on both sides over the first stapling and staple again. Continue like this until you reach the other end, thus obtaining the classic spike closure.
Proceed in the same way with all the other disks to get your culurgiones. About thirty should be released.
Once finished all the dough and prepare all the culurgiones, prepare a light tomato sauce by frying briefly garlic and oil and then adding tomato sauce, salt and basil.
Meanwhile cook the culurgiones, a few at a time, in boiling salted water for about 5-6 minutes (depending on the thickness of the dough): when they rise to the surface you can drain them.
Arrange the culurgiones in the dish, season with the tomato sauce, decorate with fresh basil and serve.
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