Preheat your oven to 175C / 350F. Spray the bottom of three 8-inch cake tins with oil spray and line with baking paper. Set aside.
To a large bowl, add the cake flour, salt and baking powder. Use a whisk to combine. Set aside.
To a separate bowl, add the butter, 1 1/3 cups of the caster sugar and vanilla extract. Use an electric hand mixer to whip until pale and fluffy, about 3 minutes. Add the coconut milk and vegetable oil, and mix on low speed to begin with then up to medium high speed until well combined.
Add the dry ingredients and mix until a batter forms.
To a separate large mixing bowl add the egg whites and use clean beaters to whip for 10 seconds until frothy. Add the cream of tartar and whip until soft peaks form. While the mixer is on high speed, add the remaining 2/3 cup of caster sugar a little at a time. Once all the sugar is In there, continue whipping for 2 minutes until stiff glossy peaks form.
Add the egg yolks and use a spatula to fold through.
Add half the egg mixture to the batter and fold through until well combined. Add the remaining egg mixture and repeat.
Split the batter between the three cake tins and bake for 20 minutes or until a toothpick inserted into the center comes out clean Once baked, allow to cool in the cake tins