
Preheat oven to 350F (175C) and line a 12-count muffin tin with paper liners. Set aside.
In a large mixing bowl, use an electric mixer to cream together the sugar, butter, and oil until creamy and well-combined.
Add eggs and extracts and stir batter on low-speed until well combined.
In a separate, medium-sized bowl, whisk together flour, baking powder and salt.
Alternate adding the flour mixture and the coconut milk to the butter mixture, starting and ending with the flour mixture. Gently stir together with a spatula after each addition until just combined (there may be some small lumps in your batter but all flour should be absorbed – take care to not over-mix).
Evenly divide batter into prepared muffin tin.
Transfer to center rack of 350F (175C) preheated oven and bake for 17-19 minutes, until a toothpick inserted in the center of the toothpick comes out clean or with a few moist crumbs.
Allow cupcakes to cool in their tin for 5 minutes before carefully removing to a cooling rack to cool completely before frosting.
Combine cream cheese and butter in a large mixing bowl and use an electric mixer to beat on low-speed until smooth, creamy and lump-free.
Gradually add powdered sugar, about one cup (125g) at a time, mixing well between each addition until sugar is thoroughly combined.
Add coconut and vanilla extract and stir to combine. Spread or pipe frosting over cooled cupcakes