In a food processor, pulse the flour, sugar and salt until mixed. Add the butter and pulse until the butter is the size of peas. With the motor running, pour the water through the feeder tube and process until the dough has formed. Pat the dough into a 1-inch-thick disk and cover with plastic wrap. Let the dough rest in the refrigerator for at least 1 hour or overnight.
Take the dough out of the refrigerator and let it warm slightly. On a well-floured work surface, roll out the dough into a 1/8-inch thick circle about 12 inches in diameter. Transfer the dough to a 9-inch pie plate. Trim the overhang to 1-1/2 inches using scissors. Fold under and crimp the dough at the edge to create a border. Place the pie shell in the refrigerator for 30 minutes.
Preheat the oven to 375 degrees F. Prick the bottom and sides of the pie shell with a fork. Line the shell with aluminum foil and fill with pie weights or dried beans. Fold over the foil to expose the sides of the shell. Bake for 25 minutes until the pie has started to turn golden brown. Remove the foil and weights and bake for an additional 15 minutes. Take the crust out of the oven and set aside. Reduce the oven temperature to 350 degrees F.
To make the filling, combine the sugar, melted butter, flour, cocoa powder, corn syrup and vanilla extract. Beat in the eggs and whisk until the mixture is fully combined. Stir in the chopped pecans and pour the filling into the pie shell. Bake for 35-40 minutes. The filling will still seem a little wobbly, but it will set once it cools. Transfer the pie to a wire rack to cool.
For the salted caramel topping, bring the sugar, water and lemon juice to a boil in a small saucepan. Do not stir. When the mixture starts to turn brown, gently swirl the pan. Once the color is deep golden brown, remove from the heat. (This will take about 8 minutes. Make sure to watch the pan.) Pour in the heavy cream while stirring continuously. When the bubbling has stopped, stir in the butter until it has melted. Add the kosher salt.
Pour the caramel over the pie and let it cool for 15-20 minutes before sprinkling with flaky sea salt. Decorate the top with the pecan halves.