How to Make It
In a large bowl, combine the flour and salt. Cut in the butter until the mixture resembles coarse crumbs. Work in the shortening and add 1/4 cup plus 1 tablespoon ice water. Gather the dough into a ball. Divide the dough in half and flatten each piece into a 6-inch disk. Wrap in plastic wrap and refrigerate for at least 30 minutes.
Preheat the oven to 450°. In a large bowl, combine the peaches, 1/2 cup of the sugar, the lemon juice and tapioca.
On a lightly floured surface, roll out one piece of dough into a 14-inch circle. Fit into a 9-inch pie pan without stretching; trim the edge, leaving about a 1/4 inch overhang; reserve the scraps. Roll out the second piece of dough to a 14-inch circle.
Add the raspberries to the peaches. Using a slotted spoon, scoop the filling into the pie shell, leaving most of the accumulated juices behind. Brush the rim of the dough lightly with some of the beaten egg, Place the second dough circle on top and press gently to seal. Trim the edges, leaving 1/2 inch over the rim; fold the dough under and flute it, if desired.
From the reserved scraps of dough, cut out some decorative shapes for the top of the pieelongated leaves or miniature peaches. Using a sharp knife, cut at least several steam vents into the top crust. Brush the crust with the beaten egg and arrange the pastry cutouts on top. Brush again with the beaten egg and sprinkle the pie with the remaining 1 tablespoon sugar.
Bake the pie for 15 minutes. Reduce the oven temperature to 350° and continue to bake for 40 to 45 minutes longer, or until bubbling and golden brown on top. Let the pie cool for at least 3 hours before serving.