Make Crust: In a bowl or food processor, combine flour, sugar, and salt. Cut in cold cubed butter until pea-sized crumbs form. Drizzle in ice water 1 tablespoon at a time until dough just comes together. Form into a disk, wrap in plastic, and chill in refrigerator for 30 minutes.
Prep Apple Filling: In a medium bowl, gently toss sliced apples with brown sugar, lemon juice, cinnamon, nutmeg, and cornstarch until evenly coated.
Roll & Arrange: Preheat oven to 400°F (200°C). Roll chilled dough on parchment paper into a 12-inch circle (about 1/8 inch thick). Arrange spiced apples in concentric circles in the center, leaving a 2-inch border of bare dough around the edges.
Pleat & Egg Wash: Gently fold the pastry border up and over the outer edge of the apples, pleating every 2 inches. Brush folded dough with egg wash and sprinkle generously with turbinado sugar.
Bake to Golden: Slide parchment with galette onto a baking sheet. Bake at 400°F for 35 minutes until pastry is deep golden brown and apple juices are bubbling.
Drizzle & Serve: Cool for 10 minutes. Drizzle warm salted caramel sauce generously over the apples and crust, sprinkle with flaky sea salt, slice into wedges, and serve warm with vanilla ice cream.