In a medium bowl, add the dark chocolate cocoa powder, both of the sugars and the salt. Whisk together until well mixed.
While continuing to whisk, add the milk and the cream. Continue to whisk all ingredients until fully combined and the cocoa powder is completely dissolved. Make sure the cocoa powder doesn't have any lumps.
Add the vanilla and whisk again.
Pour the mixture into a freezer safe container, cover it and place container in the freezer. Allow ice cream to freeze for at least 2 hours.
Sit ice cream out for 5 to 10 minutes allowing it to soften before serving.
Notes
If you do have an ice cream maker then you can enjoy your ice cream much faster. We also added some mini chocolate chips to ours before freezing, but that's optional.