Prepare the crust. Line a large baking sheet with parchment paper. Roll the pie crust into approximately a 12-inch circle and transfer it to the prepared baking sheet. Refrigerate while you prepare the fruit.
Make the filling. In a large bowl, gently combine the sliced peaches, blueberries, brown sugar, cornstarch, lemon juice, lemon zest, vanilla, cinnamon, and salt. Let the mixture sit for about 5 minutes.
Fill the galette. Remove the crust from the refrigerator. Spoon the fruit into the center, leaving about a 2-inch border around the edges. Try to leave excess liquid behind in the bowl so the bottom of your galette stays crisp.
Add the butter. Scatter the little pieces of cold butter over the fruit.
Fold the crust. Gently fold the edges of the dough up and over the filling, overlapping the dough slightly as you work around the galette. The center should remain open.
Chill. Refrigerate the assembled galette for about 20 minutes. Meanwhile, preheat the oven to 400°F.
Finish the crust. Whisk the egg with the milk or cream. Brush it over the exposed crust and generously sprinkle with coarse sugar.
Bake. Bake for 38–45 minutes, or until the crust is deeply golden and the fruit filling is bubbling in the center.
Cool. Allow the galette to cool on the baking sheet for at least 20–30 minutes before slicing. This gives the fruit juices time to thicken.
Serve slightly warm or at room temperature with vanilla ice cream, whipped cream, or a little powdered sugar.