Preheat the oven to 375 degrees F (190 degrees C). Halve peaches and remove pits. Slice thinly.
Combine peach slices, brown sugar, lemon juice, cornstarch, and cinnamon in a bowl. Set aside.
Roll pie dough out on a lightly-floured work surface to about 1/8-inch thick. Use a 6-inch bowl or round cutter to cut out 4 circles of dough. Refrigerate until ready to assemble.
For frangipane: add pistachios, powdered sugar, flour, and salt to a food processor. Pulse three times, until crumbly. Add butter and vanilla extract and pulse until combined. Add 1 egg and process until it has a spreadable consistency.
To assemble galettes, spread 2 tablespoons frangipane onto each circle of pie dough, then arrange 6 to 7 peach slices on top, leaving a 1 inch border. Fold the sides of the dough up and over the filling to make a 1/2-inch border.
Whisk remaining egg and milk together in a small bowl for egg wash; brush pie dough with egg wash and sprinkle with coarse sugar.
Bake in the preheated oven until golden brown, 28 to 32 minutes. Remove and let cool for 5 minutes.
Serve warm with a scoop of vanilla ice cream.
