Start by preheating your oven to 350°F (180°C) and lining a baking sheet with parchment paper.
In a medium saucepan, combine ¾ cup chopped mangoes, ¾ cup chopped peaches, ½ cup sugar, 2 tablespoons cornstarch, ¼ teaspoon cinnamon, 1 tablespoon lemon juice, and ⅛ teaspoon salt.
Heat this mixture over medium-high heat, stirring often. Once it starts boiling, reduce the heat and let it simmer for 5 minutes until it thickens. Remove from heat, stir in ½ teaspoon vanilla extract, and let it cool completely.
While the filling cools, dust your counter with flour and roll out your first pie crust. Using a 3½-inch round cookie cutter, cut out 8 circles. Repeat with the second pie crust for a total of 16 circles.
Mix one beaten egg with 1 tablespoon of heavy cream to make your egg wash.
Place 1 tablespoon of the cooled peach-mango filling in the center of 8 pie circles. Leave a ½-inch border around the edges.
Brush egg wash around the edge of each filled circle, then cover with the remaining circles. Press the edges together with your fingers, then seal by crimping with a fork.
Cut two small vent holes in the top of each pie. Brush the tops with egg wash and sprinkle with turbinado sugar.
Place the pies on your prepared baking sheet and bake for 25 minutes, or until the crust is golden brown and you can see the filling bubbling through the vent holes.
Let the pies cool on the baking sheet for 15 minutes before moving. They can be served warm or at room temperature.
Store any leftover pies in an airtight container at room temperature for 2 days, or freeze for up to 3 months.