Peach Filling:

1. In a large saucepan, add the peaches, granulated sugar, brown sugar, salt and cinnamon. Toss to coat the peaches evenly with the sugar.
2. Bring the mixture to a simmer over medium heat until the peaches are tender enough to mash. Mash about half of the peaches.
3. Continue simmering the peaches until the juices have reduced and begin to thicken.
4. Stir in the butter, lemon juice, and vanilla extract until fully combined.
5. If needed to thicken further, sprinkle cornstarch over the peaches and continue stirring until the mixture thickens. Remove from heat and allow to cool.

Pie Dough:

1. In a medium bowl, combine the flour, sugar, and salt. Whisk to combine.
2. Place the flour, salt, and sugar in the bowl of a food processor fitted with a steel blade and pulse a few times to mix. Add the butter and shortening. Pulse 8 to 12 times, until the butter is the size of peas. With the machine running, pour the ice water down the feed tube and pulse the machine until the dough begins to form a ball.
3. (Alternately if not using a food processor): Cut in the butter and shortening with a pastry blender or fork until the mixture resembles coarse meal.
4. Gradually add ice water, 1 tablespoon at a time, until the dough gathers into a well-formed ball. You may need more or less ice water. With floured hands, mix and squeeze the dough until it forms a ball. Knead it several times to combine, but be careful not to over-knead, as this can make the dough tough.
5. Cut the dough into 8 equal-sized pieces and roll each piece into a ball.
6. Place the dough balls on a baking sheet and press them into discs. Cover with plastic wrap and refrigerate until well chilled, at least 30 minutes but no more than 5 days.

Cinnamon-Sugar:

1. Combine the cinnamon and sugar in a shallow dish, such as a pie plate, and whisk until well mixed. Set aside.

Egg Wash

1. Whisk together egg and 1 tablespoon water and set aside.

Assembling the Pies:

1. On a well-floured surface, place one dough ball. Gently roll it around in the flour. Flour a rolling pin and roll each dough ball out into six-inch circles.
2. Place two heaping tablespoons of filling in the center of each dough circle.
3. Brush edges with egg wash and fold the dough over the filling, crimping all around the half-moon edges with a fork to seal well.
4. Frying the Pies:
5. In a large heavy iron skillet, Dutch oven, or deep fryer, add at least 2 inches of soybean or vegetable oil (if using a deep fryer, follow the manufacturer's instructions for filling with oil).
6. Heat the oil to 375°F, using a thermometer to keep the temperature regulated.
7. Carefully place 2 to 3 pies into the hot oil, making sure they have enough room and do not overlap each other.
8. Fry the pies for 1-2 minutes per side, until lightly golden brown.
9. Using a slotted spatula or slotted spoon, remove the fried pies and place them on a paper towel-lined baking sheet. Allow to cool until slightly warm and easy to handle.

Finishing:

1. After the pies have drained and cooled slightly, sprinkle them on both sides with the cinnamon-sugar mixture.
2. Place the pies on a cooling rack to continue cooling.
3. Serve warm or at room temperature.
4. Store in an airtight container at room temperature for up to 2 days or in an airtight container in the refrigerator for up to 5 days.