Prep. Take the pie crust out of the refrigerator and let it soften slightly so it’s easier to roll. Line a large, rimmed baking sheet with parchment paper.
Prep apples. Peel the apples, remove the cores, and slice them into ¼-inch thick pieces.
Make filling. Place the sliced apples in a large bowl and add the brown sugar, lemon juice, cinnamon, vanilla, salt, and nutmeg. Toss well until everything is evenly coated and the brown sugar starts to dissolve. Set aside for 5–10 minutes while you roll out the pie crust and prepare the egg wash.
Make egg wash. Beat the egg with a teaspoon of water in a small bowl.
Preheat oven to 375°F (190°C).
Roll the crust. On a lightly floured surface, roll out the pie dough into a 13-inch circle and gently transfer it to the prepared baking sheet. Check the crust for any small tears — if you find any, gently pinch or press them together to seal. This helps prevent the juices from leaking out while the galette bakes.
Fill. Toss the apples to mix them. Use a slotted spoon to lift the apples from the bowl, leaving the excess juices behind. Arrange the apples in the center of the dough, leaving a 2-inch border around the edges. Reserve the remaining juice for later.
Shape. Carefully lift one edge of the dough and fold about 2 inches over the apples. Continue folding around the galette, overlapping the dough every couple of inches. Gently pinch the pleats to hold them in place, but avoid pressing the dough into the fruit.
Brush and Bake. Brush the unbaked crust with the egg wash, then sprinkle it with coarse sugar. Bake for 50 minutes to 1 hour, or until the crust is a deep golden brown in color.
Finish. Transfer the pan to a wire rack and brush the remaining apple juices over the baked crust, dabbing some over the apples as well.
Serve. Serve the galette warm or at room temperature with vanilla ice cream, or enjoy the leftovers chilled straight from the fridge—it’s delicious either way.