Preheat the oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Combine the sliced apples, cranberries, brown sugar, granulated sugar, cinnamon, nutmeg, vanilla, lemon juice, cornstarch, and salt in a large bowl. Toss until everything is evenly coated and let the filling rest for about 10 minutes.
Roll the pie dough into a 12-inch circle on a lightly floured surface, then transfer it to the prepared baking sheet.
Spoon the fruit filling into the center of the dough, leaving about a 2-inch border around the edges. Fold the edges of the dough over the filling, overlapping slightly to create a rustic galette.
Whisk together the egg and milk, then brush the exposed pastry with the egg wash. Sprinkle the crust with coarse sugar.
Bake for 38 to 42 minutes, or until the crust is deeply golden and the fruit is bubbling.
Cool the galette on the baking sheet for 10 to 15 minutes before transferring it to a cooling rack. Dust lightly with powdered sugar if desired before serving.
