Add the cocoa and sugars in a medium bowl; stir to combine.

Add the whole milk and use a hand mixer on low speed to whisk or combine until the cocoa and sugars are dissolved, about 1 to 2 minites.

Stir in the heavy cream and vanilla.

If not freezing immediately, cover and refrigerate until ready to use.

Turn machine on; pour mixture into freezer bowl, and let mix thicken, about 25 to 35 minutes.

The ice cream will have a a soft, creamy texture. If a firmer consistency is desired, transfer the ice cream to an air tight container and place in the freezer for about 2 hours.

Remove from freezer abiut 15 minutes before serving.