Make the dough: In a bowl, mix flour, sugar, and salt. Cut in cold butter using a pastry cutter or fork until it looks like coarse crumbs. Add ice water 1 tablespoon at a time until the dough just comes together. Form into a disk, wrap, and chill for 30 minutes.
Prepare the apples: In a bowl, toss the sliced apples with brown sugar, granulated sugar, cinnamon, nutmeg, lemon juice, flour, and vanilla. Let sit while the dough chills.
Roll and assemble: Roll out dough into a 10–12 inch circle on parchment paper. Arrange apple slices in the center, leaving a 2-inch border. Fold the edges over the apples, pleating gently.
Brush and bake: Brush the crust with egg wash and sprinkle with sugar. Bake at 190°C (375°F) for 35–40 minutes until golden brown and bubbly.
Cool and serve: Let the crostata cool for 10–15 minutes. Serve warm with a drizzle of honey or a scoop of vanilla ice cream.