
In a food processor, combine the flour, sugar and salt. Pulse a few times to combine. Add the butter. Pulse 3 to 4 times to break the pieces down a bit. Slowly pour in 4 tablespoons of water while pulsing the food processor. The dough should hold together when pinched. If not, add another tablespoon or two of water.
Turn out the dough onto a lightly floured surface and work it gently into a ball. Flatten the dough into a disc, wrap tightly with plastic wrap, and refrigerate for at least 1 hour or up to 3 days.
Preheat the oven to 425°F. Line a large rimmed baking sheet with parchment paper.
In a large bowl, stir together the peach slices, lemon juice, and vanilla extract. Add the sugar, cornstarch, and cinnamon, and toss until the peaches are well coated in sugar.
On a lightly floured surface, roll the pie dough into a 12-inch circle and place on the parchment paper.
Spoon the filling into the center of the crust leaving a 2-inch border of dough around the filling. Reserve and extra juices from the peaches in the bowl.
Fold the crust up and over the filling towards the center, covering just the edge of the filing, leaving most of the filling exposed Pinch any folds or overlaps in the dough to help it keep its shape. Drizzle any juices from the peach bowl over the filling. Brush the crust with egg wash, and sprinkle with coarse sugar, if desired.
Bake for 30 minutes or until the crust is a deep golden brown and the filling is bubbling. Let the galette cool for 15 to 20 minutes before slicing and serving.