You need to make the pie dough at least 2 hours before making the pie. You can make it up to 24 hours beforehand and store it in the refridgerator, or you can make it up to 3 months beforehand and freeze it. Defrost frozen dough in the refrigerator for 24 hours before using for this recipe.
In a small bowl, dissolve the salt into the water. Place the bowl in the refrigerator until you need to use it.
Cut the butter into small, pea-sized chunks.
Add the flour and butter to the food processor. Working quickly, pulse the mixture until it forms into large crumbs and some of the pieces of butter remain pea-sized.
Drizzle about half the salted water over the flour mixture. Pulse several times.
Drizzle the rest of the salted water over the mixture and pulse several more times. The dough will come together in the food processor. As soon as it comes together, transfer the dough from the food processor onto a clean, lighly floured surface.
Divide the dough into 2 equal balls.
Working quickly, shape each ball into a round disk about 1” thick.
Completely wrap each disk in plastic wrap, then refrigerate them for a minimum of 2 hours. You can make the dough a day ahead and refrigerate for up to 24 hours.
Reserve the egg until later. You will use this as an egg wash right before you bake the assembled hand pies.