Preheat oven to 325°F.
Line three 6-cup muffin pans with cupcake liners.
If you don't have an official double boiler, suspend a metal or heat-proof bowl across the top of a pan with a little simmering water in the pan. Make sure the bottom of the bowl or pan doesn't come in contact with the water below. Put the white chocolate in the bowl and stir until melted and smooth.
Beat the sugar, butter, and vanilla in large bowl with an electric mixer.
Add 1/3 of the flour mixture and then 1/3 of the coconut milk, and stir.
Repeat until everything is thoroughly mixed.
Divide the batter evenly among the muffin cups.
Place the white chocolate buttons in the frosting to your aesthetic preference and enjoy!