*Canned coconut milk will cause syrup to separate when stored, so shake syrup to combine before using. Or substitute the 1/2 cup canned coconut milk and 1/2 cup water with 1 cup coconut milk beverage brand, like Silk or So Delicious. Also, 1/2 cup roughly crushed lime leaves is a small handful, about 1/8 oz. To double this recipe, you'll need 1/4 oz. lime leaves.
Whisk sugar, coconut milk and water together in a small saucepan. Bring mixture to a boil, stirring to make sure sugar dissolves, and cook for 1 to 2 min. Remove from heat and add lime leaves and and star anise. Cover and allow mixture to steep until room temperature, about 20 min. Strain and store in a sealed container in the refrigerator. Use within 2 weeks.