To extract thick coconut milk, place grated coconut in a food processor. Add 2 cups water. (Grind in batches depending on the size of the food processor).
Transfer ground coconut to a muslin cloth placed over a sieve. Place the sieve on a bowl. Gather the sides of the muslin cloth and squeeze out coconut milk. This is the first extract or thick coconut milk.
To extract thin coconut milk, place coconut back in the food processor. Add 1 cup water. Grind to coarse paste. Transfer to the muslin cloth and squeeze again to get the second extract of coconut milk also called thin coconut milk.
If you want more thin coconut milk, repeat the process.
Fresh coconut milk can be stored in an airtight container in the refrigerator for up to 4 days. You can also freeze coconut milk, but it may separate. Just thaw it in the refrigerator and reblend before using for cooking purposes.