For the filling - Stir the fruit, sugar and corn starch together in a small, non-reactive saucepan. Bring to a boil over medium heat and cook, stirring, until translucent, about 10 minutes. Set aside to cool completely, a few hours or overnight.
For the pastry- Mix the flour, salt and baking powder in a large bowl. Add the butter. Using a pastry blender or your fingers, cut the butter into the flour until the mixture resembles coarse bread crumbs with some pea-size pieces of butter. Gradually stir in enough of the water, and the vinegar, for the dough to clump together. Gather up the dough and divide into two portions, one slightly larger than the other. Press each half into a thick disk, wrap in plastic wrap, and refrigerate until chilled but not hard, 1 to 2 hours.
To bake the pie - Preheat the oven to 400 - 425 F. On a lightly floured work surface, roll out the larger portion of dough into a 1/8-inch-thick round. Transfer to a 9-inch pie dish, trimming the dough to a 1/2-inch overhang around the edges of the dish. Roll out the remaining dough into a 1/8-inch-thick round, and center over filling. Pinch the edges of the dough layers together, and flute the edges. Cut a few slits in the top crust. Brush with the whisked egg for a shiny appearance.
Baking pies can vary a bit from oven to oven. It is best to have some familiarity with the heat or with the conduction of heat, in your oven. In general, set a rack in the center of the oven, place pie on the rack at 400 - 425 F and cook for 15 minutes, then reduce the temperatureto 350 to 375 F and continue cooking, without opening the door, for another 20 - 25 minutes. At this point you should check to see if the edges of the pie are browning too much. If so, place a pie collar or aluminum foil over the exposed crust and continue baking until the center is golden and bubbly, between 15 and 25 more minutes.
Cool for at least an hour for best results - the pie will still be warm and the corn starch and fruit will have time to gel.