Place the flour, cocoa, powdered sugar and salt in the bowl of a food processor. Blend for a few seconds until well combined. Add the butter and pulse until it looks like a coarse meal, then add the cream and egg. Pulse until just combined. Dump onto a lightly floured surface and use your hands to form the dough into a disc. Cover with plastic wrap and place in the fridge for an hour.
Line the bottom of a 9 inch false bottom tarte pan with parchment. Remove the dough from the fridge and allow to sit a few minutes until its warmed up enough to roll out. Roll out the dough on a floured surface to a diameter to fit the pan plus a couple inches for the sides. Roll the dough around the rolling pin, then lift it over the pan and gently unroll it. Use your hands to gently ease the dough into the tart pan, making sure it goes tightly into the corners and up the sides. Cut off any excess. Prick the bottom of the tart dough all over with the tines of a fork. Place the pan into the freezer for 15 minutes while you preheat your oven to 375. Place the tarte pan onto a sheet tray then into the preheated oven and bake for 20 minutes. Remove and turn the heat down to 350.
Filling
Whisk together the egg yolks, granulated sugar, salt and vanilla.Pour the milk, cream and espresso into a medium saucepan and slowly bring it to a simmer.Once it reaches a simmer, slowly drizzle a third of the milk into the egg mixture while whisking. Then pour the warmed egg and milk mixture back into the saucepan and heat till just under 170 degrees, stirring constantly. Strain the custard through a fine mesh strainer to remove the espresso grounds. Pour the custard into the partially baked crust and very carefully place the tart in the oven. The filling is still very runny and can easily slosh around, so go slowly. Bake until the filling is just set, approximately 25 minutes. If it still jiggles, let it go a couple more minutes. Remove from the oven and allow to cool completely before serving.