Flip the chilled can of coconut milk over and open from the bottom. The liquid will now be at the top. Discard or save for a smoothie. We won't be using it in this recipe today.
In a chilled bowl of an electric mixer, add the stiffened coconut from the can and whip until smooth and fluffy.
Add the powdered sugar and peppermint extract.
In a small saucepan, heat the non-dairy milk or creamer so it is hot, but not boiling. Almond or coconut milk will work just fine. Whatever you have on hand.
Add the white chocolate chips and whisk until melted and you have a nice, fluid mixture. Cool this mixture.
Gently fold the white chocolate mixture into the whipped "cream" mixture, trying to maintain as much of the incorporated air as possible.
Spoon into chilled glasses and top with crushed vegan-friendly peppermint candies.