Preheat your oven to 325 degrees F. Spray an 8×8 square inch cake pan with cooking spray, line with parchment paper, and spray again. Set aside.
In a medium-sized bowl, whisk or sift together the cake flour, baking powder, and salt. Set aside.
In the bowl of a stand mixer, fitted with the paddle attachment, cream the butter, oil, and sugar on medium high speed until light/fluffy and smooth, about 3 minutes. With a rubber spatula, scrape down the sides and cream again for 1-2 more minutes.
Add the eggs and the egg whites, one at a time, beat on medium-speed until, after each addition, until well incorporated (around 30 seconds after each egg) Once all the eggs have been added, beat on medium speed high for 1 minute. Add the coconut extract, sour cream, and mix on low, just until incorporated.
With the mixer on the lowest speed, add half of the flour mixture to the liquid mixture followed by ½ of the coconut milk. Add the rest of the flour mixture, and then the rest of the coconut milk, Don’t over mix. Only mix until incorporated and the batter is smooth! Scrape the bottom and sides of the bowl to ensure the batter is evenly mixed.
Add the the batter to the prepped pan, and carefully smooth the batter with a small offset spatula and bake until a toothpick comes out clean, or with only a few crumbs on it, about 35-40 minutes. Depending on your oven.
After they are out of the oven, I let mine cool for 15 minutes. Then I transfer the cake onto a wire rack to finish cooling in the fridge or freezer to help speed up the process. (20 minutes in the freezer, 30 minutes in the fridge)
While the cake is cooling, make the frosting.
For the Cream Cheese Frosting
In a blender or food processor, finely grind up the freeze dried strawberries until the resemble a fine crumb. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the softened cream cheese on medium speed until smooth and creamy. With a rubber spatula, scrape down the sides and the bottom of the bowl. Add the butter and cream on medium high speed for 1 minute.
Add the sifted powder sugar, vanilla, salt, freeze dried strawberries, and cream, mix on low until incorporated. Turn the speed to medium high and beat for 2 minutes.
Depending on how you like your frosting, if it’s too thin, add a little more powder sugar. If too thick, add a dash more heavy cream.
Once the cake has completely cooled, use an offset spatula, spread the frosting evenly over the top of the cake.