Adapted from the Craft of Baking
For the chocolate sable dough:
1 cup plus 2 tablespoons flour
1/4 cup unsweetened cocoa powder
1/4 teaspoon salt
10 tablespoons butter, chilled and cubed
1/3 cup sugar
2 tablespoons beaten egg
For the filling:
First make the dough. Sift together the flour, cocoa powder and salt in a bowl. Using an electric mixer fitted with the paddle attachment, mix the butter and sugar on low speed until there are no visible pieces of butter remaining, 2-4 minutes. Add the egg and mix just until incorporated. On low speed, add the flour mixture in three parts, mixing each in completely before adding the next. Turn out the dough onto a lightly floured surface and shape into a flattened disk. Wrap in plastic and refrigerate for at least 1 hour.
On a lightly floured surface, roll out the dough to an 11 inch round. Press dough into a 9 1/2-inch tart pan with a removable bottom. Trim the excess dough right to the top edge of the pan. Prick the bottom of the dough all over with a fork, and freeze until firm about 10 minutes.
While dough is chilling, preheat the oven to 350 F. Line the tart shell with aluminum foil, leaving a 1 inch overhang, and fill it with pie weights or dried beans. Place the tart pan on a baking sheet and bake for 15 minutes. Remove the foil and pie weights, rotate the baking sheet and continue baking until the crust feels dry to the touch, 15 to 20 minutes. Put the baking sheet on a wire rack and cool crust completely.
Reduce oven temperature to 275 F.
Combine the bittersweet and semisweet chocolates in a mixing bowl. Pour the cream, milk and sugar into a small saucepan and bring to a boil, stirring until sugar dissolves. Pour about a third of the cream mixture over the chocolate and slowly whisk together until the chocolate is completely melted. Add the remaining cream and whisk to combine. Set aside.
Mix the eggs in a bowl with vanilla extract until very well beaten. Pour a third of the chocolate mixture over the eggs and gently whisk just to combine. Return the egg mixture to the chocolate mixture, add the salt, and whisk until smooth.
Fill the crust with the chocolate mixture. Bake, with tart pan still on the baking sheet, rotating the baking sheet halfway through, until the edges of the custard are set and the center is slightly soft, about 30 minutes. Transfer the tart to a wire rack and let cool completely. Serve tart at room temperature. The tart is best eaten the day it is made but can be kept at room temperature covered in plastic wrap for up to 2 days.