Prepare dough:
In a medium bowl, whisk together flour, salt and sugar until well combined.
Cut chilled shortening into the flour mixture until it resembles coarse crumbs.
Add water and mix until a stiff dough forms.
Form into a disc, cover in plastic wrap and chill for at least 1 hour.

Peach filling:
In a medium saucepan, combine peaches, sugar, flour, lemon juice and cinnamon. Cook over medium heat until the mixture thickens. Remove from heat and stir in vanilla. Set aside to cool.

Preheat oven to 375°F and line a sheet pan with parchment paper.
Roll out the chilled pie dough to 1/8–1/4 inch thick. Cut bottoms and tops using a 2.5- or 3-inch round cookie or biscuit cutter. Place rounds on the prepared cookie sheet.

Place 1 Tbsp. of the peach filling in the center of each dough round. (Depending on your cutter size, you may need more or less filling. Avoid overfilling.)
Cover with a second dough round. For best results, roll the top pieces slightly larger to stretch over the filling. Press edges to seal and use a fork to crimp.

For the egg wash, whisk together the egg and water. Brush the tops of each hand pie with the egg wash.

Optional: Sprinkle with Demerara sugar.