bowl of an electric mixer, cream together the butter, sugar and vanilla until very light and fluffy, about 3 minutes.
melt the white chocolate in a double boiler. when it's just warm to the touch, stir it into the butter mixture on low speed, just until combined--it may separate a bit, but it will come back together. with the mixer on low, alternate adding the flour mixture and the coconut milk in three batches until well-blended. transfer the batter to a medium bowl.
clean and dry the bowl of the mixer. whip the egg whites on medium high speed until they reach soft peaks, about 4 minutes. gently fold the egg whites 