Deepest-dish apple pie

Ingredients:
1 cup sugar
1/2 tsp ground cinnamon
1 tsp ground cardamon
6 tbsp butter 15 apples, peeled, cored, and cut into eights (about 8 pounds)
3/4 tsp pure vanilla extract
6 tbsp Calvados or brandy
1/2 cup plus
2 tbsp heavy cream
1 Pate Brisee
1 large egg yolk

Preparation:
1. In a small mixing bowl, combine the sugar, cinnamon, and cardamon. Set sugar mixture aside. 2. In a skillet, melt 2 tablespoons butter over medium-high heat. Add one-third of apples, one-third of the sugar mixture, and 1/4 teaspoon vanilla. Saute until apples turn golden brown, about 4 minutes. Remove skillet from heat.
3. Measure 2 tablespoons Calvados into a cup, and add to skillet. Return skillet to heat, and cook 3 minutes. Add 3 tablespoons cream; cook, stirring until thick, 2 to 3 minutes. Transfer cooked apples to a large bowl.
4. Repeat steps two and three two more times with the remaining of apples.
5. On a lightly floured surface, roll out pate brise 3 to 4 inches larger than the ovenproof bowl (mine is four 1/2 inches deep and 10 inches wide), to an 1/8-inch thickness. Punch a hole in the center of the dough.
6. Place the apples mixture in the ovenproof bowl; drape rolled out pastry over the top, trim overhanging edges of to create a scalloped edge. Decorate top with any trimmings, using cold water to adhere.
7. In a small bowl, mix the egg yolk and the remaining tablespoons cream; brush mixture over dough. Chill 30 minutes.
8. Heat oven to 400 degrees F or 200 degrees C. Bake pie until golden brown, 50 to 55 minutes. After 30 to 40 minutes, place a piece of aluminium foil over top to prevent further browning, and continue baking until pie bubbles.
Transfer to a wire rack to cool, 1 hour.