Sift cake flour into a large mixing bowl, then add baking powder and salt and whisk mixture. In the bowl of an electric stand mixer, fitted with the paddle attachment, blend together granulated sugar, butter and canola oil on medium speed until well combined. Scrape down bowl.
Add in egg yolks one at a time and mix until combined after each addition (reserve 2 egg whites), then mix in coconut and vanilla extracts. Scrape down bowl.
Add 1/3 of the flour mixture, blend just until combined. Add half of the coconut milk, mix just until combined. Mix in another 1/3 of the flour mixture followed by remaining coconut milk. Finish by mixing in last 1/3 of the flour mixture.