Whisk milk, cream, sugar, cocoa, and salt in a saucepan until smooth.

Warm over medium heat, stirring, until steam rises and sugar dissolves.

Add chopped chocolate and stir until melted and smooth.

Remove from heat and stir in vanilla. Cool to room temperature.

Chill mixture in fridge at least 2 hours, then freeze in an ice cream maker per maker instructions.

Transfer to a container and firm in freezer 2–4 hours before serving.