Preheat the oven to 350°F (175°C).

In a mixing bowl, combine the flour, cocoa powder, and powdered sugar. Add the cold, cubed butter and mix with a pastry cutter or your fingers until it resembles coarse crumbs.

Stir in the beaten egg until the mixture comes together. If the dough is too crumbly, add ice water a little at a time until it forms a dough.

Roll out the dough on a floured surface to fit the tart pan. Transfer the dough to the pan, gently pressing it into the bottom and sides. Trim any excess dough hanging over the edges.

Prick the bottom of the crust with a fork and refrigerate for about 15 minutes.

Once chilled, bake the crust in the preheated oven for 15 minutes. Remove from the oven and let cool slightly.

In a small saucepan, heat the heavy cream over medium heat until just boiling. Remove from heat and add the chopped chocolate, stirring until melted and smooth.

In a separate bowl, whisk together the eggs, sugar, vanilla extract, and salt until combined. Slowly mix in the chocolate mixture until smooth.

Pour the filling into the pre-baked tart crust, smoothing the top with a spatula.

Bake the tart in the oven for an additional 15-20 minutes until the filling is set but slightly wobbly in the center.

Allow the tart to cool at room temperature, then chill in the refrigerator for at least 2 hours before serving.