Pre-heat the oven to 350°F and prepare a 9" pie plate.
Make the pie shell by flouring both sides of your dough and placing it on a floured surface. Roll out the dough until it measures approximately 1/8 inch thick by 12 inches in size. Transfer the disk to a pie dish. Fold over any excess and crimp edges if necessary. Use a fork to poke holes in the bottom of the pie crust. Then, gently press aluminum foil against the dough. Bake for 25 minutes, adding pie weights or dried beans.
Remove the shell from the oven. Carefully remove foil and pie weights. Bake the crust for another 10-15 minutes, or until it is golden brown. Allow to cool completely on a rack.
Add milk and chocolate to medium saucepan on medium heat. Stir frequently until the chocolate is melted. Do not boil. Allow to cool.
Combine the cocoa powder, cornstarch, and salt in a small bowl. Keep aside until you are ready to use.
Use a stand mixer with a paddle attachment or a large bowl to beat the egg yolks and sugar on medium-high speed, until they are thickened and pale yellow. Mix in the cocoa powder mixture. Slowly add the milk mixture to the mixer at low speed.
Place the contents of your stand mixer bowl into a medium saucepan. Heat on medium. Slowly whisk the mixture until it becomes thickened. This should take approximately 6-8 minutes.
Don't overheat. As it cools, the pudding will begin to thicken. Stir in the butter and vanilla. Allow to cool on a rack for a few minutes.
Place the pudding in the cooked pie shell. Smoothen the top using an offset spatula. Let it cool on the counter for a while. Place in a plastic wrap and place in the fridge. Cover the pie with plastic wrap and refrigerate for at least 6 hours or until it is completely chilled. Enjoy with whipped cream.