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1
Combine the flour, salt, warm water, and olive oil, then knead for 10 minutes until the dough is smooth and uniform — the warm water encourages the gluten to develop quickly, so the dough becomes supple rather than tight and resistant. Wrap it and rest for 30 minutes at room temperature so the network of gluten relaxes and the dough will roll and stretch without tearing or pulling back. It is ready when it is supple and no longer springs back under the heel of the hand.
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2
Roll the rested dough to a sheet approximately 5 mm thick and cut into strips of approximately 5 mm width. Working one strip at a time, roll each strip between the palms and the board, pressing and extending outward from the centre, so the strand lengthens evenly from the middle rather than thinning at one end only, until a long cylinder of 3–5 mm diameter is formed. The thickness will be uneven along the length; this irregularity is the mark of hand-made pici — uniform cylinders indicate machine production — so lay the finished pici on a lightly floured surface without pressing them together.
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3
This is where the dish lives or dies. Place the sliced aglione cloves in a wide pan with the olive oil over the lowest possible heat and cook for 20–25 minutes, stirring occasionally, so the garlic surrenders its sharpness gradually and the oil carries that sweetness through the whole sauce rather than leaving it locked in the clove. The cloves must remain pale throughout; the moment they colour, bitterness enters the sauce and cannot be corrected. At 25 minutes over very low heat, the garlic will have transformed from sharp and pungent to sweet and creamy, almost dissolving into the oil.
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4
Add the crushed San Marzano tomatoes to the softened garlic and oil, season with salt and dried chilli, and simmer over moderate heat for 15–20 minutes so the tomato loses its raw edge and the garlic and oil bind with it into a single, cohesive sauce. The sauce should reduce slightly until it is unified and deeply sweet-garlicky, with no sharp or separate note. Taste for salt before you pull it from the heat.
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5
Bring a large pot of well-salted water to a full rolling boil and cook the pici until tender but with resistance at the thickest points — the irregular thickness means some sections will be slightly more cooked than others, which is characteristic of this pasta. Drain, reserving a ladleful of pasta water, so you have something starchy on hand to loosen the sauce without diluting its flavour. Toss the pici immediately in the aglione sauce over low heat, adding pasta water as needed until the sauce coats each strand in a continuous film.