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1
Combine the 00 flour and salt in a bowl. Add the olive oil and warm water. Bring together into a dough and knead on an unfloured surface for 10 minutes until smooth and elastic. Wrap and rest at room temperature for 30 minutes. The dough is ready when it springs back slowly under a fingertip.
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2
While the dough rests, make the filling. Blanch the cicoria in well-salted boiling water until tender, then drain and squeeze it with both hands until no further moisture can be extracted — this is where the dish lives or dies: any residual water in the filling will turn to steam during frying and burst the sealed seam. Combine the dry cicoria with the torn olives, drained capers, roughly chopped anchovies, peperoncino flakes, and a drizzle of olive oil. The filling must be cool and dry before assembly.
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3
On a lightly floured surface, roll the dough to 3 mm thickness. Cut rounds of 15 cm diameter. Place a compact mound of filling on one half of each round, leaving a clear border of at least 1.5 cm. Fold the dough over to form a half-moon. Press the edges firmly with the fingers first, then seal the entire border with the tines of a fork — the forchettata — pressing decisively so that the seal is true. The sealed edge should show an even, unbroken impression.
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4
Heat the olive oil in a wide, deep pan to 175–180 °C. Lower the calzoni into the oil one or two at a time without crowding. Fry for 3–4 minutes per side. The oil temperature must not fall below 175 °C — below this, the dough absorbs oil rather than crisping. The calzone is ready to turn when the underside is deep golden and the dough has begun to puff; it is done when both sides are evenly golden and the surface is blistered and rigid to a light tap with tongs.
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5
Lift the calzoni from the oil and drain briefly on a rack — not paper, which traps steam and softens the crust. Serve immediately. Within minutes of frying the crust begins to lose its rigidity; the calzone must be eaten hot from the oil.