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For the pie dough: Combine the flour, sugar and salt in the bowl of a food processor and mix. Add the butter cubes and process until the largest pieces are the size of peas and the smallest are the size of a grain of rice (or use a pastry cutter). Transfer to a bowl and slowly pour in 1/4 to 1/2 cup ice water, a few drops at a time, mixing vigorously with your hands in between pours; the butter and flour mixture should just come together.
Divide the dough into two equal pieces, shape into discs and wrap tightly in plastic wrap. Let rest, refrigerated, for at least 1 hour.
Roll one piece of dough into a circle just larger than the pie pan you will be using. Fit the dough into the pan, fold the edges under and crimp as you like. Put this pastry shell in the freezer while you make the pie filling.
For the filling: Whisk together the sugar and whole eggs and yolks in a medium bowl until fully incorporated. Add the dark corn syrup, melted butter and bourbon and mix to combine. (The mixture should be completely smooth and homogenous. The butter will rise to the top rather rapidly if you let the mixture sit, but you can whisk it back together in a few seconds.)
Brush the frozen pastry shell with the melted chocolate using a pastry brush, spreading it evenly over the bottom and sides. Scatter the pecans over the bottom of the pastry shell and pour the sugar and egg mixture over the pecans.
For the egg wash: Mix the beaten egg with a splash of cream. Brush the sides of the pastry crust with the egg wash.
Bake until the filling has puffed up and cracked and the crust is golden brown, about 45 minutes. All home ovens are different, so if the pecans start to burn, turn the oven down to 325 degrees F to finish baking, or tent some aluminum foil over the pie to prevent more unwanted darkening. You also may need to rotate the pie mid-bake, if one side is browning more rapidly than the other.
Let cool for at least 2 hours before eating.