2tablespoonschopped dark or milk chocolateoptional
Place dark chocolate and milk chocolate into a microwave safe bowl. Melt at 20 second intervals at 80% power in the microwave until able to stir the chocolate until smooth. Be careful not to overheat. Set aside and allow to cool.
Combine whipping cream, milk, and cream cheese, mixing until smooth. Mix in sugar, cocoa powder, melted chocolate from earlier, and vanilla. If using optional chocolate pieces, stir them in as well.
Pour into ice cream maker container and make according to ice cream maker directions.
Once ice cream has churned, remove from the ice cream maker container and serve immediately as soft serve or place in an airtight container in the freezer for 1 hour to overnight for a firmer ice cream.