Whisk the cocoa powder together with about half the sugar in a medium saucepan. Add the milk a little at a time, whisking after each addition, until the mixture is completely smooth with no lumps. Whisk in the cream and the salt.
Set the pan over medium low heat. Whisk gently and heat until the mixture just begins to steam and the cocoa is fully bloomed. Pull the pan off the heat, add the chopped chocolate, let it sit undisturbed for one full minute, then whisk until glossy and completely smooth.
In a separate bowl, whisk the egg yolks with the remaining sugar until pale and slightly thickened.
Temper the yolks. Ladle about one cup of the hot chocolate dairy into the yolks in a slow steady stream while whisking constantly. Once combined, pour the yolk mixture back into the saucepan.
Return the pan to medium low heat. Stir constantly with a rubber spatula, dragging it across the bottom of the pan, until the custard reaches 170 to 175 degrees Fahrenheit. Do not let it boil. Use the thermometer rather than the spoon test, because the chocolate causes the base to coat a spoon well before the yolks are cooked.
Set up an ice bath. Fill a large bowl with ice and a splash of cold water, then nest a smaller clean bowl inside it. Pour the custard through a fine mesh strainer directly into the inner bowl. Add vanilla extract.
Stir every few minutes until the custard stops steaming and cools to about room temperature or chilled.
Cover the custard and refrigerate at least 4 hours, best 8 hours or overnight, until fully cold.
Stir the vodka into the cold base if using. Pour into the ice cream maker and churn 40 to 60 minutes, until it thickens to soft serve consistency and mounds on the paddle.
Transfer to a chilled shallow container. Press a piece of parchment directly against the surface of the ice cream, cover with the lid, and freeze at least 4 hours or until scoopable.