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1
Combine the flour and salt in a large bowl. Dissolve the yeast in the warm water and pour it into the flour with the 30 ml of olive oil. Mix vigorously with a wooden spoon or by hand until a very soft, sticky, uniform batter forms — it should be wetter than bread dough and pull reluctantly from the sides of the bowl. The dough is ready when no dry flour remains and the mass is cohesive but clings to everything it touches.
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2
Cover the bowl with a cloth and leave at room temperature until the dough has doubled in volume and its surface is domed, blistered, and visibly aerated. This is where the dish lives or dies: an under-proofed dough will produce dense, heavy fritters that never achieve the airy, slightly chewy interior that defines pittule. Do not rush this stage.
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3
Pour the frying oil into a deep, heavy pan to a depth of at least 6 cm and heat to 170–180 °C. Verify the temperature with a thermometer or by dropping a small piece of dough into the oil: it should rise immediately to the surface and begin to colour within 30 seconds.
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4
Oil your hands generously. Pull an irregular lump of dough — roughly the size of a walnut — away from the mass and drop it directly into the hot oil. For stuffed pittule, press a single olive, a piece of anchovy, a caper, or a small spoonful of tomato sauce into the dough ball before it enters the oil. Work in batches of five or six; the fritters need room to puff and must not crowd the pan.
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5
Fry, turning once, until the fritters are deeply golden-brown on all sides and have developed a craggy, irregular exterior. Lift with a slotted spoon and drain briefly on kitchen paper. The interior should be soft and airy when torn open; a pale or smooth exterior signals oil that is too cool.
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6
Serve immediately. Scatter plain pittule with flaky salt. Dust the sweet version with caster sugar or drizzle with vincotto. Pittule deflate and toughen as they cool; they are eaten standing, directly from the pan.