In a medium heatproof bowl with a pour spout (I use a large glass liquid measuring cup), whisk the egg yolks and cornstarch together with a fork or small whisk. It will be *very* thick. Set aside.
Combine the milk, heavy cream, sugar, and salt in a medium saucepan set over medium heat. Whisk until all the sugar has dissolved, then bring to a gentle simmer, whisking occasionally.
Once simmering, remove about 1/2 cup (120ml) of the warm milk mixture and, in a slow and steady stream, whisk into the egg yolk and cornstarch mixture. Keep those egg yolks moving so they don’t scramble. In a slow and steady stream, pour and whisk the egg yolk mixture into the saucepan. The pudding will immediately begin to bubble and thicken. Stand back and use caution as the bubbles may burst. Cook for 1 full minute, whisking constantly.
Remove the pan from heat and whisk in the butter. Then whisk in the chopped chocolate, espresso powder, and vanilla. You will have about 3 and 1/2 cups of filling. If you notice a lot of little chunks of egg yolk, they may not have been tempered properly. To fix, you can run the warm custard through a fine mesh sieve.
Allow to cool for 10 minutes. I do not recommend any longer than this, as it will be too thick to spread neatly into the crust.
Spread filling into cooled pie crust. (A small offset spatula is helpful for this.) Cover tightly with plastic wrap and refrigerate for at least 4–6 hours or overnight, until chilled and thickened. Pie may be refrigerated for up to 2 days before serving