Make the crust: In a large bowl, combine the flour, salt, and sugar. Add the cold butter and use a pastry cutter or your fingers to cut the butter into the flour until the mixture resembles coarse crumbs. Gradually add the ice water, stirring until the dough comes together. Divide the dough in half, shape each half into a disk, and wrap in plastic wrap. Refrigerate for at least 1 hour.

Preheat the oven to 375 degrees F (190 degrees C).

Make the filling: In a large bowl, combine the peaches, strawberries, sugar, cornstarch, vanilla extract, almond extract (if using), and lemon juice. Stir until the fruit is evenly coated.

Assemble the pie: On a lightly floured surface, roll out one of the dough disks to fit a 9-inch pie dish. Transfer the dough to the pie dish and trim the edges, leaving a 1-inch overhang. Fill the pie crust with the fruit filling. Roll out the second dough disk and place it over the filling. Trim, fold, and crimp the edges. Cut slits in the top crust to allow steam to escape. Brush the top crust with the beaten egg and sprinkle with sugar.

Bake the pie: Bake for 50-60 minutes, or until the crust is golden brown and the filling is bubbling. If the edges of the crust start to brown too quickly, cover them with aluminum foil.

Cool and serve: Allow the pie to cool on a wire rack for at least 2 hours before serving. This allows the filling to set. Serve the pie with a scoop of vanilla ice cream, a dollop of whipped cream, or a drizzle of custard, if desired.