Hi Jansen,
I am COOCOO for Coconut Milk! I love it and drink it all the time.
Here are 3 different ways to make a starch free batch of coconut milk:
1. Puree 1 cup organic dried unsweetened shredded coconut with 4 cups water in a vitamix or blender. Strain through a nut milk bag (basically just a nylon bag) and drink the milk, use it in soups, and then dehydrate the left over "pulp grinds" left in the bag and make coconut flour. This makes my most favorite kind of coconut flour, which I perfer much more than the store bought stuff.
Andrea
I was going to say "try coconut milk" so I will just tack a bit onto Andrea's great suggestions:
Pour very hot or boiling water over the shredded coconut and
let it sit until it is room temperature - that way you extract more of the volatile coconut oils from the mix and that seems to give you better 'dried leftovers' to grind, too. (you also don't burn yourself by having the top blow off the blender when you whizz it up! - No, I have not found this out the hard way

... just trying to prevent anybody else from doing it! )
Either way - yum yum!