In a medium bowl, whisk together the dark cocoa powder, sugars, and salt.
While whisking, add the milk and the cream. Whisk together until completely combined, and the cocoa is completely dissolved with no lumps.
Add the vanilla and combine.
Pour the ice cream mixture in your ice cream maker, and process according to manufacturer's instructions.
Notes
Hersey's Special Dark Cocoa is what I use. It's easy to find, so I'm sure you can get it, too.
I use a Cuisinart Ice Cream Maker, and you just freeze the canister the ice cream is made in. It takes about 15 minutes to make ice cream with no salt and ice to mess with. I love it!
If you like a harder ice cream, put the ice cream in a freezer container and cover. Let it freeze for at least 2 hours, and then let it sit on the counter for 10 minutes before serving. The ice cream straight out of the maker is just like soft-serve. Out of the freezer, it is like store-bought.
If you like a less "dark" chocolate, reduce the cocoa powder to 1/3 cup.