Special equipment: a 3-inch round cutter
For the pastry: In the bowl of a food processor, combine the flour, granulated sugar and salt and pulse to combine. Add the butter and pulse until the mixture resembles coarse meal with some bigger pieces of butter. Add the ice water and pulse just until the crumbs begin to come together. Add a little more water if necessary but try not to add too much. Turn the mixture out onto a big sheet of plastic wrap, form it into a disc, wrap it and refrigerate for at least 1 hour.
Preheat the oven to 375 degrees F.
On a lightly floured surface, roll out the dough to an even 1/8- to 1/4-inch thickness. Using a 3-inch cookie cutter, cut out 16 to 20 circles. Transfer to a rimmed baking sheet and chill while you make the filling.
For the filling: In a small saucepan, combine the peaches, granulated sugar and cornstarch. Bring to a boil over medium heat, mashing the peaches with a fork, and cook until the mixture has thickened, 6 to 8 minutes. Stir in the bourbon to taste. Let cool completely, about 30 minutes.
In a small bowl, whisk together the egg and salt. On a rimmed baking sheet lined with parchment, lay out half of the dough discs. Dollop 1 to 2 tablespoons of the filling in the center of each disc. Brush around the edges of the pastry with some of the egg mixture. Top with another dough disc, pressing the edges with a fork to seal. Brush the tops with the egg mixture and sprinkle with coarse sugar. With a paring knife, make a little slit in each pie to vent steam.
Bake until golden brown, 25 to 30 minutes. Transfer the pies to a rack to cool or serve warm.