Step 1: In a large bowl, whisk together the flour, salt, and 1 tablespoon of sugar. Add the cold cubed butter and use a pastry cutter to incorporate until it resembles coarse crumbs.
Step 2: Gradually add ice water, one tablespoon at a time, mixing until the dough just starts to come together. Form into a disk, wrap in plastic, and refrigerate for at least 1 hour.
Step 3: Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Step 4: In a medium bowl, toss the sliced apples with lemon juice, brown sugar, cinnamon, and nutmeg until well coated.
Step 5: On a floured surface, roll the chilled dough into a 12-inch circle. Transfer the dough to the prepared baking sheet.
Step 6: Arrange the apple slices in the center of the dough, leaving a 2-inch border around the edges. Fold the edges of the dough over the apples, pleating as you go.
Step 7: Brush the edges of the crust with the beaten egg wash and sprinkle with coarse sugar. Bake for 40-45 minutes until the crust is golden brown and the apples are tender.
Step 8: Let the galette cool for at least 15 minutes before slicing and serving.