In a medium saucepan, whisk together the cream, cocoa powder, sugar, and salt. Bring to a gentle boil, whisking occasionally, then reduce the heat and simmer for 30 seconds.

Remove from the heat and add the chopped chocolate. Whisk until smooth, then whisk in the milk and vanilla.

Pour into a heatproof bowl and let cool to room temperature. Cover and chill in the refrigerator for at least 2 hours or overnight.

Remove the chilled chocolate ice cream base from the fridge and whisk well. Churn in an ice cream maker according to the manufacturer’s instructions, typically 20 to 30 minutes. The ice cream will be soft after churning. For firmer ice cream, transfer to an airtight container and freeze for 2 to 4 hours before serving.

Store in an airtight container in the freezer for up to a month. If the ice cream is too firm to scoop straight from the freezer, let sit at room temperature for a few minutes to soften.