In a large bowl, whisk together the all-purpose flour, sugar, and salt until well blended. Cut in cold unsalted butter using a pastry cutter until the mixture resembles coarse crumbs. Gradually sprinkle in ice-cold water, mixing gently until a cohesive dough forms. Shape into a disk, wrap in plastic wrap, and refrigerate for 1-3 hours.

Prepare the filling by combining brown sugar, lime juice, vanilla extract, cinnamon, ginger, cornstarch, and a pinch of salt in a medium bowl, stirring until blended. Fold in sliced peaches, ensuring each slice is coated. Let the filling sit while you roll out the dough.

Preheat your oven to 400°F (200°C). On a floured surface, roll out the chilled dough into a 12-inch circle about 1/8-inch thick. Transfer the dough to a parchment-lined baking sheet. Spoon the peach filling into the center, leaving a 2-inch border around the edges. Fold the edges over the filling, pleating as you go, then brush the crust with the egg wash.

Refrigerate the assembled Peach Galette for 20 minutes. Bake for 35-40 minutes, or until the crust is golden brown and the filling is bubbly. Rotate the baking sheet halfway through for even baking.

Let the galette cool slightly on the baking sheet. After about 10-15 minutes, slice and serve warm, possibly with a dusting of powdered sugar or a scoop of vanilla ice cream.