Preheat oven to 350 degrees. Line cupcake tin with cupcake liners.
Sift together cocoa powder, flour and baking powder. In another bowl whisk together sugar, eggs, vanilla, vegetable oil and 3/4 cup coconut milk. Gradually whisk flour mixture into sugar mixture.
Fill cupcake liners 2/3 full. Bake in preheated oven for 12 – 15 minutes or until a toothpick inserted comes out clean.
Allow to cool for several minutes in the cupcake tin. Transfer to a cooling rack to cool completely.
While cupcakes are cooling make the frosting by melting the coconut spread and unsweetened chocolate together over low heat. Remove from heat and allow to cool.
Once cooled, whisk together chocolate mixture and 1 1/2 cups powdered sugar. Stir in remaining 1/4 cup coconut milk. Frosting will become thicker as it cools. If you would like it a little thicker, add more powdered sugar until desired consistency.