Adapted very slightly from Dining In by Alison Roman
Preheat oven to 375. Line two rimmed baking sheets with parchment paper
Roll the pie dough on a lightly floured surface about 1/8 inch thick (no thicker than 1/4 inch). Transfer dough to parchment-lined sheet and chill in the freezer for 5 minutes (this will make the dough easier to work with).
Make an egg wash by beating the egg with 1 teaspoon water. Set aside.
In a small bowl, combine the raspberries, peaches, sugar, lemon zest, and thyme. Mix gently to combine and set aside.
Using a 4 1/2 inch ring cutter (or the rim of a water glass), cut out 16 circles. Place 8 circles on the baking sheet and place in the freezer to cool for a few minutes. Using your rolling pin, roll out the remaining 8 circles to be slightly larger in circumference (by about 1/2 an inch).
Remove the smaller circles from the freezer and place a large spoonful of peach-raspberry mixture in the center of each one. Brush egg wash around the edges of each circle. Place a 1/4 inch cube of butter on the top of each fruit pile.
Place the larger dough circles on top of the smaller ones, pressing the edges down around the fruit. Using the tines of a fork, press to seal the pies. Brush the tops of each pie with egg wash and sprinkle generously with Demerara sugar. Using a sharp paring knife, cut a few slits in the top of each pie to allow steam to escape.
Place the pies in the oven and bake until the juices start bubbling and the crust is, as Alison says, "deliciously golden brown, the color of a perfect croissant," about 25 to 30 minutes. Let cool before devouring.