Whisk the egg in a small bowl and set in the fridge. Preheat the oven to 350 F.
Slice the peaches in thin, lengthwise slices. Store in the fridge until ready to use.
Take one disc of dough out of the fridge about 15 minutes before you want to use it. Since we're cutting the dough into four pieces, it can be a little bit cooler than we would normally like it when rolling it out.
Dust your work surface and rolling pin with flour. Cut the dough into four roughly equal pieces. Form each of the smaller pieces into a ball before you roll it out.
On the floured surface, roll out the dough into a roughly 5-6 inch circle, turning the dough after each time you roll it out. The circle doesn't have to be perfect; that's part of the charm.Repeat this process for all of the dough until you have 8 circles. I do recommend doing four at a time, leaving one dough ball in the fridge while you assemble the first four galettes. Arrange the four crusts on your work surface. Add 1/4 cup of blueberry compote, or just under that amount, to the middle of the crust. Fan the peach slices on top of the compote. It might take a bit of arranging, but don't worry about being perfect.
Once you've got the peaches added, fold the edges of the crust around the fruit. It will naturally leave the middle open, which is what we want. The crust should cover just the sides. Brush the edges of the crust with the egg wash and sprinkle with coarse sugar. Move the assembled galettes onto a baking sheet lined with parchment paper using a spatula. Store them in the fridge while you repeat the assembly process with the second dough ball.Once you're done assembling the second set of galettes, add them to the fridge as well. I like to bake each tray on its own. This promotes more even baking. Arrange the baking rack so it's just above the middle and add your tray there. Bake for 30 minutes at 350 F.
The crust will be lightly golden brown when they're done, and the crust will be firm with some give to it. The blueberry compote will be nice and bubbly. The peach slices will have retained their shape but will be very soft.
Let them cool for ten minutes before enjoying, preferably with a scoop of ice cream, although I really enjoy them when they're cold as well.