Place both the can and carton of coconut milk in the fridge for at least 24 hours.
Also, place your mixing bowl and whisk in the fridge at least 10 minutes before you start the frosting. This will help whip the coconut cream.
For the can of coconut milk, open it from the bottom, drain the liquid and spoon the coconut cream into your mixing bowl.
Open the carton of coconut milk, and spoon the coconut cream from the top to your mixing bowl. See notes if the coconut cream did not separate.
Mix the coconut cream at medium-high speed with your stand mixer for about 3 minutes.
Add 4 tablespoons of icing sugar to start, and mix on medium-high speed. Add more icing sugar, if desired (to taste). Mix on high speed until the frosting stiffens.
If the frosting is too stiff, add some of the liquid in the carton of coconut milk, one tablespoon at a time, then mix on high speed. Keep adding liquid until you reach your desired frosting softness.
Finally, add the vanilla extract, then mix.
If you want, you can add matcha powder to the frosting to have matcha coconut frosting. Keep in the fridge until ready to use.