Preheat the oven to 375 degrees F. Stir together the cherries, sugar, cornstarch, and lemon juice. Set aside.
To make the dough, pulse the flour, sugar, salt, and butter in a food processor until coarse crumbs form. Add the water and form into a dough. Add a little more water if needed.
Roll out the dough to a large rectangle about ¼ inch thick and cut out circles or squares (for circles, I used an inverted circular Tupperware container). Re-roll the dough and continue cutting until you have 10 circles. Place five of the circles on a baking sheet and divide the cherries among them (reserve the excess juice). Cover with the other five circles, crimp closed, and cut vents in the top. Spoon the cherry juice into the pies through the air vents. Brush with egg wash.
Bake in the middle of the oven for 40-45 minutes, or until golden.