Preheat the oven to 350 degrees.
To prepare the peaches, boil a large pot of water. Place the ripe peaches in the boiling water for 30 seconds, then transfer them to a cold water bath for a few seconds. Remove the peaches from the water and pull off the skin. If it doesn’t come off easily, it means the peaches aren’t ripe enough for this method. (Peel with a vegetable peeler instead.) Cut the peaches in half and remove them from their pits. Cut them into very thin slices and place them in a large bowl. Add the raspberries, coconut sugar, lemon juice, vanilla extract, and flour to the bowl. Stir to coat evenly.
To make the crust, place the flour, salt, cold butter, and coconut sugar in a food processor fitted with a dough blade. Pulse several times to make a crumbly mixture. Then add the ice water one tablespoon at a time until the dough comes together. It should bind together easily, but it shouldn’t be sticky. If you add too much water, you can add a little more flour to dry it out.
Roll out the crust to 1/8 inch thick on a piece of floured parchment paper. Transfer the crust to a baking sheet with sides and carefully remove the parchment paper. Using a slotted spoon, place the fruit mixture in the center of the crust (you can discard the excess liquid). Spread the fruit out in an even layer, leaving about two inches of crust around the outer edge. Wrap the edges up on top of the fruit, leaving a circle of fruit exposed in the middle. Sprinkle with an extra teaspoon of coconut sugar if desired.
Bake for 40 to 45 minutes, or until the crust is beginning to brown and the peaches are tender. Cool on a wire rack before removing the galette from the baking sheet.