In a heatproof bowl, combine the coarsely chopped semisweet chocolate and the tablespoon of butter. Set this bowl over a pot of simmering water, ensuring the bowl doesn’t touch the water. Stir occasionally until the chocolate and butter are completely melted and smooth. Remove from heat and set aside.
In a medium saucepan, combine the heavy cream and whole milk. Heat the mixture over medium heat until it begins to steam, but do not let it boil. Stir occasionally to prevent scorching.
In a separate bowl, whisk together the egg yolks, sugar, and salt until the mixture is pale and slightly thickened.
Once the milk mixture is heated, gradually pour about a cup of the hot milk into the egg yolk mixture while whisking continuously.
Pour the tempered egg mixture back into the saucepan with the remaining milk. Cook over medium-low heat, stirring constantly, until the mixture thickens and coats the back of a spoon. This should take about 5-7 minutes. Do not let it boil.
Remove the saucepan from heat and add the melted chocolate mixture and vanilla extract to the thickened custard. Whisk well until fully combined and smooth.
For an ultra-smooth texture, pour the pudding through a fine mesh strainer into a clean bowl.
Cover the surface of the pudding with plastic wrap to prevent a skin from forming. Let it cool to room temperature before refrigerating for at least 4 hours or until set.
