Preheat the oven to 325ºF (165ºC). Grease 2 silicone 6-serving mini hemisphere pans. Place the pans on large baking sheet.
In a medium-sized bowl, sift together the flour, baking powder and salt until well blended.
In a large bowl, beat the butter, sugar and oil together with an electric mixer at medium speed, until pale and fluffy. Beat in the coconut extract. Gradually beat in egg whites, until the mixture is well combined, stopping to scrape the sides of the bowl.
On low speed, beat in the flour mixture in three additions, alternating with the coconut milk, stopping to scrape the sides of the bowl as needed.
Fill the hemisphere pan wells, 2/3 full with batter. Bake for 20-24 minutes, until a toothpick inserted into the center of cakes comes out clean.
Place the silicone pans on a cooling rack to cool for 10 minutes. Invert the pans to remove mini cakes and place on cooling racks to cool completely.