Preheat your oven to 350 degrees.
Remove a dough disc from the refrigerator. You will work with one at a time, so it is best to leave the dough in the refrigerator, until you are ready to assemble.
On a lightly floured piece of parchment paper, roll out one disc until it is about 12 inches in diameter, and about 1/4 inch thick.
Dust off any excess flour, and place the parchment paper, with dough round on top of it, onto a baking sheet.
Sprinkle the dough with 2 tsp. of sucre vanillé.
Arrange 1/2 of your peach and sugar mixture onto the dough round, leaving a 1 1/2 inch border free of filling.
Scatter one half of the butter pieces (about 1 tbsp) over the top of the peaches.
Fold the dough border over the peach mixture, overlapping as you go.
Place in the refrigerator for 15 minutes to chill, and repeat these steps with the remaining dough disc and filling.
In a small bowl, whisk together egg yolk, and milk to make an egg wash.
Remove your galette from the refrigerator, after it has chilled for 15 minutes.
Using a pastry brush, lightly brush the egg wash over the dough. If you would like, you can sprinkle 1 tsp. of sugar over the egg washed dough.
Bake for 35-40 minutes. Baking time may vary from oven to oven. You want to bake the galette until the crust is golden, and the peach filling is bubbling.
Place the baking sheet on a wire rack to cool. Serve warm, or most commonly, at room temperature.