For the Crust:

1. Sift the flour, sugar, cocoa powder, and salt into a large bowl. 
2. Using a pastry cutter, cut the cold butter cubes into the dry ingredients until a uniform mixture forms with small, coarse crumbs.
3. Using your hands, knead in the egg just until a crumbly dough forms, adding a teaspoon of water at a time if the dough seems too dry.
4. Turn the dough onto a clean counter dusted with flour and press lightly to form a smooth, flat disc. Tightly wrap the disc in plastic wrap and refrigerate for at least 1 hour.
5. Set out a 9-inch tart pan with a removable bottom. Remove the chilled dough from the refrigerator and let sit at room temperature for 5-10 minutes, until it has softened slightly and is pliable. Remove the plastic wrap and place the disc on a clean counter dusted with flour.
6. With a rolling pin, roll and flatten the dough until it is about 1/8 inch thick, and large enough to cover the width of the base with about an inch of excess on all sides.
7. Carefully transfer the dough to the tart pan. Press into the bottom of the pan, then press into the sides. Trim any excess dough around the edges so it’s flush with the top of the pan.
8. Place the pan in the freezer and chill for 1 hour until very cold and firm.
9. Preheat the oven to 400°F. Cover the bottom and sides of the tart pan with a sheet of parchment paper and fold the excess over the sides for easy lifting later. Gently press the paper against the bottom and sides of the pan. Add pie weights so they nearly reach the top of the pan, and spread them out evenly. 
10. Transfer the pan to the oven and bake for 15-20 minutes, or until the edges of the crust are just starting to dry out. Carefully remove the pan from the oven, and avoid pressing the bottom of the pan so the crust doesn’t separate from the sides. Lift the parchment paper to remove the hot pie weights and set the weights aside to cool.
11. Lightly pierce the dough covering the bottom of the pan several times all over with the tines of a fork. Place the pan back in the oven and bake for another 10-15 minutes, until the dough is completely baked and the surface looks dry. Remove the pan from the oven and let cool completely on a wire rack, about 1 hour. Carefully remove the shell from the pan and place on a flat plate, stand, or serving platter.

For the Ganache:

1. Place the chopped chocolate in a medium-size heatproof bowl and set aside.
2. Heat the heavy cream in a medium-size saucepan over medium heat. As soon as it begins to simmer, in about 5-8 minutes, immediately remove from the heat and pour over the chocolate. Allow to stand for 3-5 minutes, then gently stir with a whisk until the chocolate has melted completely and the mixture is smooth.
3. Add the cubed butter and gently stir until completely melted and fully combined.
4. Immediately pour the ganache into the cooled tart shell. Transfer the tart uncovered to the refrigerator and chill until completely cooled and set, about 2 hours.
5. Remove the tart from the refrigerator, slice, and serve.