Before you start to mix this up, be sure you pre-freeze the ice cream canister that goes with your ice cream maker; if you don't, your ice cream won't freeze.
In a large mixing bowl, whisk together the cocoa powder, sugar, brown sugar, and salt.
Whisk in the whole milk, mixing 'til the sugars and cocoa powder dissolve, about 1-2 minutes.*
Whisk in the cream and vanilla extract.
Turn on the ice cream freezer, and pour the mixture into the freezer bowl with the churn paddle in place.
Then place the cover on top, and let it mix 'til it thickens, about 20-25 minutes.
When the ice cream has a soft, creamy texture, it's ready. Turn off the machine, and scoop the soft-serve chocolate ice cream into bowls for serving; or if desired, scoop it into an airtight container, and place it in the freezer for 2-3 hours to firm up more. Then serve when ready.
*This step is important; I usually recommend extra whisking, just to make sure your ice cream isn't grainy. You want all of the sugars and cocoa powder to dissolve in the milk.