Whisk unsweetened cocoa powder with 1/4 cup granulated sugar in a saucepan, then whisk in heavy cream and whole milk until smooth. Heat over medium, whisking until the mixture is steaming, about 5 minutes, and look for tiny bubbles around the edges.

Add finely chopped dark chocolate to the steaming cocoa mixture and whisk until fully melted and smooth, about 2 minutes, with a glossy dark look.

Whisk egg yolks with the remaining 1/2 cup granulated sugar until pale, about 2 minutes, so the mixture looks lighter and slightly thicker.

Slowly whisk the hot chocolate cream into the egg yolks a little at a time to temper, then whisk until combined and silky.

Return the mixture to the saucepan and cook over medium-low heat, stirring constantly until the custard coats the back of a spoon at 175F, about 6-8 minutes, with a thickened, nappe-like texture.

Strain the custard through a fine mesh sieve, then stir in vanilla extract and salt. Cool completely over an ice bath until the surface looks cooled and the custard is no longer warm.

Refrigerate the custard at least 4 hours or overnight, then churn in an ice cream maker until thick and scoopable, about 20-25 minutes, with a soft-serve consistency.

Transfer to a container and freeze until firm, at least 2 hours, so the ice cream holds shape when scooped.