In a medium saucepan, combine the half-and-half and heavy cream and scald over medium-high heat, until bubbles form around the edge but not boiling. Place the chocolate in a medium heatproof bowl and place over simmering water in a saucepan and heat, stirring occasionally, until completely melted and smooth. Remove from the heat. Pour hot cream mixture over the melted chocolate and whisk until thoroughly combined.
Place the yolks in a bowl, and slowly whisk in the sugar. Slowly pour the hot chocolate mixture into the egg mixture, a little at a time, whisking constantly. When incorporated, return to the saucepan, and bring to medium-low heat. cook, stirring continuously with a wooden spoon, making sure to scrape the bottom of the pan to prevent scorching, for 5-6 minutes or until thickens and coats the soon thickly. First the mixture will be loose and then it will start to get a little thicker at the bottom. As it continues to thicken, it will start to let off a little steam.
Once thickened, strain through a fine-mesh sieve into a bowl and stir in the vanilla and salt. Press a piece of plastic wrap directly on top of the pudding to prevent a skin from forming and refrigerate for at least 3 hours our until cold. Before serving, stir the pudding until smooth.