In a medium saucepan, combine the heavy cream, milk, sugar, cocoa powder, and salt. Heat over medium-low heat, whisking constantly, until the sugar and cocoa have dissolved and the mixture is smooth. Do not let it boil.

Remove the saucepan from heat and stir in the vanilla extract. Let the mixture cool to room temperature, then cover and chill in the refrigerator for at least 2 hours, or overnight.

Pour the chilled mixture into the pre-frozen bowl of your Cuisinart ice cream maker and churn according to the manufacturer's instructions, usually for 20-30 minutes.

During the last few minutes of churning, add the brownie chunks.

Transfer the churned ice cream to an airtight container, swirling in the slightly warmed chocolate fudge sauce as you go. Freeze for at least 2 hours, or until firm.