1. Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper.

2. In a large bowl, whisk together the flour and salt. Using a pastry cutter or your fingers, cut the butter into the flour mixture until it resembles coarse crumbs.

3. Drizzle in the ice-cold water, stirring with a fork, until the dough just comes together. Divide the dough in half, shape each half into a disk, wrap in plastic, and refrigerate for at least 30 minutes.

4. On a lightly floured surface, roll out one disk of dough to fit a 9-inch (23 cm) pie dish. Carefully transfer the dough to the dish, trimming the edges to leave a 1-inch (2.5 cm) overhang.

5. In a bowl, combine the shredded chicken, sun-dried tomatoes, black olives, basil, and pepper. Spread this mixture evenly over the bottom of the pie crust.

6. Roll out the remaining dough to the same size as the top of the pie dish. Place it over the filling, pinching the edges to seal. Trim away any excess dough, and crimp the edges decoratively.

7. Using a sharp knife, cut a few small slits in the top crust to allow steam to escape. Brush the top with a little bit of water.

8. Bake the pie for 45 to 50 minutes, or until the crust is golden brown and the filling is bubbling. If the edges start to brown too quickly, cover them with strips of aluminum foil.

9. Allow the pie to cool for 10 to 15 minutes before slicing. Serve warm with extra fresh basil on top if desired.