Using a handheld mixer or stand mixer fitted with the paddle attachment, beat the butter on medium-high speed until smooth and creamy, about 5 minutes.
Add 2 cups of confectioner's sugar, beat on medium-low speed until most of the sugar is moistened. Gradually add in the remaining sugar, one cup at a time, mixing well after each addition. Stop to scrape down the sides of the bowl as needed.
And the salt and the coconut milk, one tablespoon at a time, beating on medium speed until fully incorporated. You may need more or less of the coconut milk depending on how strong you'd like the flavor.
Turn the speed up to medium-high and beat until light and fluffy. Scrape down the sides of the bowl as needed.
