1. In a large bowl, combine the flour and chilled butter. Use your fingertips or a pastry cutter to work the butter into the flour until the mixture resembles coarse breadcrumbs.

2. Gradually pour in the ice water, mixing gently with a fork until the dough comes together in a shaggy mass. Press into a ball, then flatten into a disc, wrap in plastic, and chill for 30 minutes.

3. Preheat the oven to 190°C (375°F). Line a baking sheet with parchment paper.

4. Divide the chilled dough into four equal portions. On a lightly floured surface, roll each portion into a 18 cm (7 inch) circle about 3 mm (1/8 inch) thick.

5. For each pie, place one quarter of the tomatoes, salami, olives, and basil onto one half of the circle, leaving a 1.3 cm (1/2 inch) border.

6. Fold the empty half over the filling, pressing the edges together with a fork to seal tightly. Crimp the edges if desired.

7. Transfer the pies to the prepared baking sheet. Score the top lightly with a knife to allow steam to escape.

8. Bake for 25 to 30 minutes, or until deep golden brown and crisp.

9. Let cool slightly, then serve warm with extra torn basil on top.