Cut off and discard the green top of the lemon grass and the root end, leaving about a 6-inch stalk. Remove any tough outer leaves, cut the stalk into 1-inch pieces, lightly pound the stalks with the knife handle to release the flavor .
Combine the lemon grass with the coconut milk in a saucepan and simmer for 10 to 15 minutes. Do not let it boil. Remove from the heat and strain. Discard the lemon grass and reserve the milk.
Place all the ingredients, including the milk, in a blender or food processor and puree until smooth.