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1
Combine the semolina and lukewarm water. Work to a firm, smooth dough — semolina and water only; no egg. The dough must be stiffer than an egg pasta dough; it is ready when the surface is smooth and does not stick to the hand.
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2
Wrap the dough and rest it at room temperature while the filling is prepared.
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3
Boil the Agata potatoes whole in their skins until completely tender. Peel immediately while hot and pass through a mouli or mash thoroughly. Pour the olive oil over the hot potato and work it in at once — the heat allows the oil to bind evenly. The result must be smooth and homogeneous; lumpy or watery potato will burst the pasta during cooking.
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4
Add the grated semi-aged Pecorino Sardo and the finely chopped mint to the potato. Mix until the filling is uniform and dense. It must be dry enough to hold its shape when rolled; any visible moisture is excess. Refrigerate for at least 2 hours to firm the mass before filling.
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5
Roll the rested dough to a thin, even sheet — approximately 2 mm. Cut into discs of roughly 8 cm diameter. Place a compact portion of filling at the centre of each disc, leaving a clear border of bare dough all around.
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6
This is where the dish lives or dies. Fold the disc over the filling to form a half-moon. Beginning at one end of the curved edge, work along the seam with thumb and forefinger: press, fold one side of the dough over the other, advance 3 mm, press and fold again. Each fold overlaps the last. Continue without interruption to the opposite end, accumulating 20 or more folds to form a continuous braid. A fork-crimped seal is functional but destroys the structural and cultural character of the dish. The braid must be tight: a loose or gapped seal will open in the water and release the filling.
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7
Warm the olive oil in a wide pan. Add the crushed fresh tomatoes and cook over moderate heat until they collapse and the sauce loses its raw smell. Add the basil. The sauce should remain simple and light — complexity competes with the filling.
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8
Bring a large pot of salted water to a gentle simmer — never a vigorous boil. Lower the culurgiones in carefully. Cook until they rise to the surface and the dough at the thickest point of the braid is tender but still firm. Vigorous boiling unfolds the crimp and bursts the pasta.
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9
Lift the culurgiones from the water with a slotted spoon and transfer directly into the tomato sauce. Turn gently once to coat. Serve immediately.