In a large saucepan, melt butter over medium heat. Add apples, granulated sugar, brown sugar, lemon juice, cinnamon, salt, nutmeg, and cardamom. Increase heat to medium-high, and cook, stirring occasionally, until apples begin to soften and release most of their liquid, 4 to 6 minutes.
In a small bowl, whisk together cornstarch and 1 tablespoon (15 grams) water. Stir into apple mixture; cook, stirring frequently, until mixture is thick and translucent, 2 to 3 minutes. Remove from heat, and pour into a heatproof bowl. Let cool completely.
Lightly dust a sheet of parchment paper with flour; turn out All-Butter Piecrust onto prepared parchment, and roll into a 14-inch circle (about ⅛ inch thick). Transfer dough on parchment to a baking sheet, and refrigerate for 15 minutes.
Transfer cold crust to a 9-inch springform pan, pressing into bottom and up sides. Pour apple filling into prepared crust. Fold and pleat excess dough over filling, leaving center exposed. Freeze until firm, 15 to 30 minutes.
Position oven rack in bottom third of oven. Preheat oven to 425°F (220°C).
In another small bowl, whisk together egg and remaining 1 tablespoon (15 grams) water. Using a pastry brush, lightly brush egg wash onto dough. Sprinkle turbinado sugar onto dough.
Bake for 20 minutes. Reduce oven temperature to 375°F (190°C), and bake until crust is golden and apples are tender, 35 to 40 minutes more. Let cool completely in pan on a wire rack.
Carefully run a knife around sides of pan. Remove from pan, and serve immediately at room temperature. Refrigerate in an airtight container for up to 3 days.