Whisk together flour, sugar, and salt in a large bowl. Add in the chilled butter cubes and the shortening and cut them into the flour mixture using a pastry blender. Work quickly until the mixture resembles a coarse meal.
Add the apple cider vinegar and water. Stir everything until dough is almost coming together. When pressed with your fingers, the mixture should cling together.
Turn it out into a floured board. Knead just until the dough comes together. Gather it into a ball, flatten into a disc and wrap with plastic. Refrigerate dough for about 2 hours or overnight. After the chilling time, make the filling.
Make the Filling and Assemble the Peach Mango PIes
Combine mangoes, peaches, sugar, and cornstarch in a medium saucepan. Cook the mixture over medium heat and bring to a boil. Stir often until the fruits are soft and covered with a thick gel-like liquid. Set aside to cool.
Let the dough sit at room temperature for 5 minutes. On a floured board, roll it out to 1/4 inch thickness*. Using cookie cutter that is 3.5 inches in diameter, cut as many circles as you can from the dough.
To fill the dough, roll the rolling pin gently over one circle to elongate it a bit more. Spoon about a tablespoon of the filling into the center of the dough. Fold the dough over, covering the filling completely. Seal the ends and use the tines of a fork to press some decorations along the edges*. Repeat with the rest of the circles. Arrange all assembled pies on a baking sheet that is lined with parchment paper. Chill them in the fridge as you heat up the oil for frying.
Fill a heavy-bottomed saucepan with the shortening and melt over medium heat. As it melts, it should occupy about 3-4 inches of the height of the saucepan. Add more shortening as needed. Once the temperature reaches 365 F, gently place 3-4 pies in the saucepan.
Cook until the pies are lightly golden, about 2-3 minutes or less. Drain the cooked pies on a plate lined with paper towels. Repeat with the remaining pies, carefully monitoring the temperature of the oil to maintain the proper heat. If the pies brown too quickly, your oil may be too hot. Adjust the heat accordingly, as you fry all the remaining pies.
Dust pies with powdered sugar and serve warm. Store leftover pies in a paper box container or bakery paper bags at room temperature for up to 2 days.
* Percent Daily Values are based on a 2000 calorie diet.
When rolling the dough, it is important to flour the board and your rolling pin often to prevent the dough from sticking too much.
For variety, you can also do some circle shaped instead of just half-moon shapes for the pies. Spoon filling into the center of a circle dough, top it with another circle dough and seal the edges. Press decorations along the edges using the tines of a fork.
The proper temperature of the oil is critical for frying the pies. The oil should reach 365 F before adding the first batch of pies, and it should maintain the temperature all the time during frying.