This is an apple pie that manages to be both refined and rustic.
Stir together sugar, cinnamon, and cardamom in a small bowl; set aside.
Melt 2 tablespoons butter in a large skillet over medium-high heat. Add one-third each of the apples and the sugar mixture, and 1/4 teaspoon vanilla. Cook, stirring often, until apples are tender and liquid has thickened and caramelized, 8 to 10 minutes. Remove from heat. Working carefully, as alcohol may ignite, stir in 2 tablespoons Calvados. Return to heat, and cook until alcohol burns off, 30 seconds. Add 3 tablespoons cream; cook, stirring constantly, until thick, 2 to 3 minutes. Transfer apple mixture to a large bowl. Repeat with remaining apples, sugar mixture, vanilla, and Calvados, and 6 tablespoons cream, in 2 more batches.
Turn out dough onto a lightly floured work surface; roll into an 1/8-inch-thick round large enough to cover top of a 3-quart ovenproof bowl and extend 2 inches over edge. Using a 1/2-inch round pastry tip, punch out hole in center. Trim to create a scalloped edge.
Transfer apple mixture to ovenproof bowl; drape pastry round over top, centering hole and letting edges of pastry hang over sides of bowl. Decorate top with cut-out shapes from leftover dough, if desired, using cold water to adhere.
Preheat oven to 400 degrees. Whisk together yolk and remaining tablespoon cream; brush over pie. Refrigerate 30 minutes.
Bake pie until top is golden brown, 50 to 55 minutes. If top browns too quickly, loosely cover with foil. Let cool completely on a wire rack, 45 to 60 minutes. Serve with cheese, if desired.