To prepare the pastry dough, whirl flour, confectioners' sugar, and salt in food processor with the blade attachment. Add about half of the butter and whirl until no chunks remain. Add remaining slices and whirl briefly to chop them up slightly. Turn food processor on again and quickly begin drizzling ice water through the feed tube, stopping before the dough comes together. Pinch some crumbs together between your fingers; if they don’t stick together, add a bit more water and whirl briefly.
Turn the mixture out onto a large piece of plastic wrap. Use the plastic wrap to help you bring the dough together; fold the edges of the dough toward the center and press down until it holds together, taking care not to overwork the dough. Divide it in half and shape into two flat disks wrapped tightly in plastic wrap. Refrigerate for at least 30 minutes.
While the dough chills, preheat oven to 425º F. Combine filling ingredients in a large bowl and let stand for 15 minutes, stirring occasionally.
Whisk egg, water, and salt together in a small bowl and set aside.
On a lightly floured surface, roll out one of the dough rounds into a 13 to 14-inch circle. Transfer it carefully to a pie dish. Roll out remaining round into a 13 to 14-inch circle.
Add berry mixture to the pie dish and brush the overhanging edge of pie dough with cold water. Center top crust over the pie dish and seal the pie gently by pressing down all the way around the pie's edge with the bottom of a fork. Trim overhanging dough with a knife and flute the edge with your fingers, if desired. Cut steam vents in the top. Brush the top crust lightly with egg wash.
Place pie on a baking sheet to catch any overflowing juices. Bake for 30 minutes on the bottom rack of the oven. Reduce heat to 350º F and continue baking for another 45 to 55 minutes, until the crust is golden brown and the juices bubble thickly through the vents with a syrup-like consistency. If the crust browns too quickly, slip a baking sheet on the top rack of the oven to diffuse the heat.
Allow to cool completely before slicing. Serve warm.