Place the cream, cocoa, sugar, and salt in a heavy-bottomed saucepan over medium heat. Bring to a rolling boil, whisking often to dissolve sugar and incorporate cocoa.

Reduce heat to low, add chocolate, and whisk until completely smooth.

Remove from heat, add half-and-half and vanilla. Pour through a fine-mesh strainer and chill overnight.

Churn in an ice cream maker according to the manufacturers' directions. Pack and freeze in an airtight container.