Slice the butter into small pieces (each stick of butter into 16 pieces). Freeze this butter on a plate for about 10 - 15 minutes.
Next, make sure the vodka, water, vinegar and flour are all chilled as well.
Place the flour, salt and sugar in a food processor. Pulse to mix the ingredients.
Add the chilled unsalted butter and pulse a few times, until you have chickpea sized butter pieces mixed in with the dough.
Next, add the vodka and vinegar, and pulse just 3 - 4 times to mix them in. IF the mix is too dry, add the rest of the water. Pulse to mix, until there's no dry flour left. Squeeze a little of the dough in your hands to see if it comes together to form a ball. If it does, then the pie dough is ready. If it still seems dry, add another tbsp of water.
Turn out the dough onto a clean surface and bring the mixture together to form a rough dough disc. Cut the disc into two, and form two flat discs that are about 5 - 6 inches across. Wrap each disc in plastic wrap and refrigerate for at least 1 hour.
When you’re ready to make the galette, remove 1 portion of the crust from the fridge and let it soften for a bit (10-20 minutes; the dough should still be cold but malleable).
Slice each peach half into ¼ inch thick slices, or ¼ inch thick wedges.
Place the peaches in a bowl. Add the lemon juice, vanilla, salt and cornstarch, and gently toss to mix in with the peaches.
Make the egg wash while the galette is chilling in the fridge and the oven is preheating. Mix the egg yolk and milk together and set aside.
Dust your work surface with flour and place the cold (but malleable) pie dough on top. Dust the top of the pie disc with a little flour as well. Roll out the pie disc until you have a rough round-shaped disc that's about 12 inches in diameter. Then gently place this crust on a parchment paper.
Starting from the middle, place the peach slices/wedges on top of the pie dough, leaving a 2 inch border from the edge of the pie crust.
If you cut the peaches into wedges - you can arrange the peaches in circles (about 2 - 3 circles), with each wedge overlapping another.
If you sliced the peaches - arrange the peach slices together and create patterns with them starting from the center. Create a crisscross pattern with most of the slices. Use any extra slices to fill in gaps.
Sprinkle the sugar over the peach slices/wedges.
Cut any frayed edges of the pie crust. Then fold over the pie dough borders. Place the galette (along with the parchment paper) on a baking tray.
Refrigerate the galette for about 15 - 20 minutes until it firms up. While the galette is in the fridge, preheat the oven to 400°F.
When the oven is preheated, remove the galette from the fridge, and generously brush the top of the pie dough with the egg wash.
Bake in the preheated oven for about 35 - 40 minutes, until the crust is a golden brown. Remove the galette from the oven, and gently lift the galette from the parchment paper (be careful as the galette will be a little soft and delicate at this point), and place it on a baking rack to cool. This will help prevent the bottom from getting soggy.
Serve the galette while warm, or at room temperature, with a scoop of vanilla ice cream or whipped cream.
This recipe makes two pie crusts, which I find more convenient in terms of handling ingredients and is also a personal preference for me (I like to keep extra pie crust in the fridge to make other goodies!). You can either halve the recipe for pie crust to make just one, or use the remaining pie crust disc for a second galette.However, the recipe for the peach filling is for one galette.