Whisk the sifted cocoa into the cold milk in a heavy saucepan until smooth, then add the cream, 6 tablespoons of the sugar, and the salt. Heat over medium heat for 5 minutes, stirring often, until steaming with tiny bubbles around the edge, about 170°F.

Whisk the yolks, remaining 6 tablespoons sugar, and honey for 2 minutes, until pale and thick. The mixture should fall from the whisk in a slow ribbon.

Whisk 1 cup of the hot chocolate cream into the yolks slowly, a spoonful at a time, then pour everything back into the pot. The mixture should look dark and glossy.

Cook over medium low heat for 6 to 8 minutes, stirring constantly, until it reaches 175°F and coats the back of a spoon. Strain it over the chopped chocolate, then whisk until the chocolate melts and the base looks glossy, and stir in the vanilla and espresso powder.

Cool the bowl in the ice bath for 15 minutes, press plastic wrap onto the surface, and refrigerate for at least 6 hours, or overnight, until very cold.

Churn the chilled base for 25 to 30 minutes, until it looks like thick soft serve, then fold in the optional chocolate chips.

Scoop the ice cream into the chilled container, press parchment onto the surface, and freeze for at least 4 hours, until firm. Let it sit for 10 minutes before scooping.