2 sticks unsalted butter, cut into small pieces, at room temperature
5 large eggs, at room temperature
In a small bowl, sift the flour with the cocoa powder and salt. In a standing mixer fitted with the paddle attachment, beat the butter with the sugar at medium-high speed until it is well blended. Beat in the dry ingredients at low speed until just combined. Add the vanilla extract and beat just until a soft dough forms, about 5 seconds. Press the pastry into a disk, wrap in plastic and refrigerate until the dough is firm, about 1 hour.
Preheat the oven to 350°. On a floured work surface, working quickly, roll out the pastry to an 11-inch round, about 1/4 inch thick. Transfer the pastry to a 10-inch fluted tart pan with a removable bottom. Gently press the pastry over the bottom and up the side of the pan. Trim off any excess pastry. Refrigerate the shell for about 20 minutes, until firm.
Line the pastry with foil and fill with pie weights or dried beans. Bake for about 30 minutes, until almost cooked. Remove the tart shell from the oven and let cool for 15 minutes, then gently remove the foil and weights. Return the shell to the oven and bake for about 12 minutes longer, until dry. Transfer to a wire rack and let the tart shell cool to room temperature. Just before filling, refrigerate the tart shell for a few minutes until slightly chilled.
Put the chocolate and salt in the bowl of the standing mixer fitted with the whisk attachment. In a small saucepan, heat the bourbon with the sugar over moderate heat, stirring a few times, just until the sugar is dissolved; try not to let the bourbon boil. Pour the warm bourbon mixture over the chocolate. Add the pieces of butter and the eggs and beat at moderate speed until the mixture is creamy and shiny.
Set the tart shell on a large baking sheet and pour in the filling. Bake for 35 to 40 minutes, until the filling has risen and the top is cracked in places. Transfer the tart to a rack and let it cool completely. Unmold the tart and refrigerate it overnight. Using a sharp knife, cut the tart into thin wedges and serve.