Combine 1 cup heavy cream, milk, sugar, cocoa powder, and salt in a medium saucepan over medium heat. Whisk constantly until the mixture is smooth and begins to steam, about 5 minutes. Do not let it boil.

Whisk the egg yolks in a medium bowl until smooth. Slowly pour about 1 cup of the hot cream mixture into the yolks while whisking constantly to temper them. This prevents the eggs from scrambling.

Pour the tempered egg mixture back into the saucepan with the remaining hot cream. Cook over medium-low heat, stirring constantly with a wooden spoon, until the custard thickens enough to coat the back of the spoon, about 5-7 minutes. It should reach 170-175°F on an instant-read thermometer.

Remove from heat and immediately stir in the chopped dark chocolate until completely melted and smooth. The residual heat will melt the chocolate perfectly.

Strain the custard through a fine-mesh sieve into a clean bowl to remove any lumps. Stir in the remaining 1 cup of cold heavy cream and vanilla extract.

Cover the bowl with plastic wrap, pressing it directly onto the surface of the custard to prevent a skin from forming. Refrigerate for at least 4 hours or overnight until thoroughly chilled.

Pour the chilled custard into your ice cream maker and churn according to the manufacturer's instructions, usually 20-25 minutes, until it reaches soft-serve consistency.

Transfer the ice cream to a freezer-safe container, press plastic wrap on the surface, and freeze for at least 4 hours to firm up before serving.