For crust: In the work bowl of a food processor, place flour, sugar, and salt; pulse until combined. Add cold butter, pulsing until mixture is crumbly. With processor running, add ½ cup plus 1 tablespoon cold water in a slow, steady stream until a dough forms. Shape dough into a disk, and wrap in plastic wrap. Refrigerate for at least 30 minutes.

Preheat oven to 350°. Spray a 9-inch deep-dish pie plate with cooking spray.

On a lightly floured surface, roll dough into a 13-inch circle. Transfer to prepared pan, pressing into bottom and up sides. Fold edges under, and crimp as desired. Freeze for 10 minutes. Top with a piece of parchment paper, letting ends extend over edges of plate. Add pie weights.

Bake until edges are set, 12 to 15 minutes. Carefully remove paper and weights. Bake 3 minutes more.

For filling: In a medium bowl, whisk together melted chocolate, flour, 2 tablespoons granulated sugar, and 1 egg until combined. Pour into prepared crust. Refrigerate until set.

In a large bowl, whisk together corn syrup, brown sugar, melted butter, vanilla, salt, remaining 1 cup granulated sugar, and remaining 4 eggs. Stir in pecans. Pour over chocolate layer. Lightly brush crust with cream.

Bake until set, 40 to 50 minutes, loosely covering with foil to prevent excess browning, if necessary. Let cool completely on a wire rack before serving.