Combine flour, sugar, and salt in a food processor.

Add cold butter and pulse until the mixture resembles coarse meal.

In a small bowl, whisk together ice water, egg yolk, and vanilla extract.

Add the egg mixture to the processor and pulse until large, moist clumps form.

Gather the dough into a ball and flatten into a disk.

Wrap the dough in plastic wrap and refrigerate for 30 minutes.

Preheat the oven to 350°F (175°C).

Lightly butter a 9-inch pie pan.

Roll the dough out on a floured surface to a 13-inch round.

Transfer the dough to the prepared pie pan.

Fold the edges under and crimp to form a high fluted edge.

Freeze the crust until firm, about 15 minutes.

Line the crust with foil and fill with dried beans or pie weights.

Bake until the sides are set, about 20 minutes.

Remove the foil and beans.

Pierce the bottom of the crust and bake until golden brown, about 20 minutes.

Cool the crust on a wire rack.

In a small bowl, combine brandy and vanilla extract.

Sprinkle gelatin over the brandy mixture and let stand for 10 minutes.

Place chopped bittersweet chocolate in a medium bowl.

In a heavy medium saucepan, mix sugar, cornstarch, and salt.

Gradually whisk in half-and-half and egg yolks into the sugar mixture.

Cook over medium-high heat, whisking constantly, until the custard is thick and smooth and begins to boil, about 3 minutes.

Quickly add 1 1/4 cups of the hot custard to the chocolate and stir until the chocolate melts and the mixture is smooth.

Add the brandy and gelatin mixture to the remaining hot custard and stir until the gelatin dissolves.

Spread the chocolate filling evenly into the cooled pie crust.

Spread the brandy filling evenly over the chocolate filling.

Refrigerate the pie uncovered until completely cool.

In a heavy small saucepan, heat sugar and water over low heat, stirring until the sugar dissolves.

Increase the heat and boil, without stirring, until the mixture is deep amber, brushing down sugar crystals from the sides of the pan with a wet pastry brush, about 11 minutes.

Remove from heat and carefully add whipping cream (the mixture will bubble up).

Add butter and stir until smooth.

Stir over low heat until the color deepens and the caramel thickens slightly, about 3 minutes.

Mix in the toasted pecans.

Transfer the caramel-pecan mixture to a small bowl.

Refrigerate until cool but not set, stirring occasionally, about 30 minutes.

Spoon the caramel-pecan topping over the brandy layer of the pie.

Chill the pie until the topping is set, about 2 hours.

Cover and refrigerate any leftovers.