Add the following to your food processor: 1 1/2 cups all-purpose flour, 1/2 teaspoon salt, and 1 cup cold butter (cubed).
Pulse until the mixture is crumbly.
Then add 1/2 cup sourdough starter discard and continue to pulse until a ball of dough forms.
Once your dough comes together remove it from the food processor and form a disc shape with your hands. Wrap the dough in plastic wrap and place it in the refrigerator for at least 30 minutes.
While the dough is chilling, make the peach filling.
In a small bowl, stir together 1/4 cup granulated sugar, 1 Tablespoon all-purpose flour, and 1/2 teaspoon cinnamon.
Slice peaches into 1/2 inch thick slices and place them into a large bowl.
Sprinkle the peach slices with the flour mixture. Add 1/2 teaspoon pure vanilla extract and stir gently.
Place your galette dough onto a large piece of parchment paper. Using a rolling pin, roll out your dough into a circle. The size should be roughly 16 inches in diameter but there’s no need to get out your ruler.
Once you’ve shaped your dough, simply spoon the peach mixture onto the center of the dough leaving a 2-inch border around the edge.
Begin folding the outer edge of the dough toward the center. You will notice the dough beginning to overlap. This is perfect! Continue until you’ve folded the edge all the way around your dough. Brush the outer edge with an egg wash using a pastry brush.
Using the parchment paper, slide the galette onto a baking tray or round pizza stone. Bake at 350° for 25 minutes or until the edges are golden brown and the center is bubbly.