Combine flour and salt in a mixing bowl. Add cold, cubed butter and use a pastry cutter or fork to cut in the butter until the mixture resembles coarse crumbs with some pea-sized pieces.
1 1/2 cups all-purpose flour, 1/2 cup unsalted butter
Add ice water gradually, one tablespoon at a time, mixing gently with a fork until the dough just begins to come together. Gather the dough into a disc, wrap in plastic wrap, and refrigerate for at least 30 minutes.
4-5 tablespoons ice water
Preheat the oven to 425°F (220°C). Remove the chilled dough from the refrigerator, and on a lightly floured surface, roll it out into a 12-inch circle. Fit the crust into a 9-inch pie dish, trimming excess edges.
In a mixing bowl, combine chopped peaches and mangoes. Add sugar, cornstarch, cinnamon, and mix well. Let sit for 10 minutes to allow juices to combine.
3 large peaches, 2 mangoes ripe mangoes, 1/2 cup granulated sugar, 2 tablespoons cornstarch, 1/4 teaspoon ground cinnamon
Pour the fruit mixture into the prepared pie crust, spreading it evenly. Dot with small bits of extra butter if desired.
Roll out the second dough disc or prepare a lattice top if preferred. Place the top crust over the filling and trim the edges. Seal the edges by pinching or crimping. Brush the top with beaten egg mixed with water to give it a shiny, golden finish.
1 egg egg, 1 tablespoon water
Bake in the preheated oven for 45 minutes or until the crust is golden brown and the filling is bubbling through the vents. Check midway and cover edges if they brown too quickly.