In a medium saucepan, whisk together the milk, sugar, cocoa powder, cornstarch, and salt. Bring the mixture to a boil over medium heat while constantly stirring.

In a separate bowl, whisk the egg yolks until smooth. Gradually add a small amount of the hot chocolate mixture to the egg yolks, whisking constantly to temper the eggs.

Slowly pour the egg yolk mixture back into the saucepan, continuing to stir. Cook for another 2-3 minutes until the pudding thickens.

Remove the saucepan from the heat and stir in the butter and vanilla extract until smooth.

Pour the pudding into serving dishes and refrigerate for at least 2 hours before serving. Garnish with whipped cream or chocolate shavings if desired.