Start by placing your cocktail serving glass of choice in the refrigerator to chill. The White Elephant tastes best cold, and a chilled glass will accentuate and elevate the drink to a great degree. Normally, a hurricane glass will work best for this drink, but you can also choose other glasses with stems, like a martini glass.
While the glass is cooling in the refrigerator, grab an electric blender, and fill a quarter of it with finely crushed ice. Then, proceed to add in the ingredients for the drink – pour in 6 oz of white rum and 2 oz of white crème de cacao, and then follow this up by pouring 4 tablespoons of sugar, 1 cup of moist and shredded coconut, and 1 cup of coconut milk into the blender.
Secure the lid of the blender, turn it on, and pulse all the ingredients for the drink on medium speed for around 8-10 seconds, until the mixture is fully-blended, and becomes smooth and thick. At this point, if you wish, you can add a drop or two of pure vanilla extract into the blender, but this is entirely optional.
Now, remove the chilled cocktail glass from refrigerator, and strain the blended drink into it. Your White Elephant cocktail is now ready – garnish the drink with shredded coconut, and serve with a straw.