For the cake: Preheat the oven to 350 degrees F. Butter two 8-inch cake pans, then fit each with a parchment round. Butter and flour the parchment.
Separate the eggs into whites and yolks. Set the yolks aside. Beat the egg whites to stiff peaks, then set aside until ready to use.
Whisk together the flour, baking powder, baking soda and salt in a medium bowl. Beat together the granulated sugar, butter and coconut oil in a large bowl with an electric mixer or with a stand mixer until light and fluffy, about 2 minutes. Add the egg yolks, coconut cream and vanilla and beat until just combined. Alternate adding the buttermilk and flour mixture to the butter mixture, being careful not to overmix. Gently fold in the beaten whites until completely incorporated, but keeping the volume!
Divide the batter evenly between the prepared cake pans.
Bake until a toothpick inserted in the middle of the cakes comes out clean, 25 to 30 minutes.
Let cool for about 5 minutes, then invert onto a cooling rack to cool completely.
For the coconut cream cheese frosting: Meanwhile, beat the cream cheese and butter in a stand mixer or in a bowl with a hand mixer until very smooth, about 2 minutes. Add the coconut extract and salt, then slowly start to add the powdered sugar, beating it in a little at a time. Beat until all the sugar is combined and the frosting is stiff but still light and fluffy. Add more sugar if it is too loose, or a little milk if it is too thick. Set aside at room temperature until you are ready to decorate.
If the cakes have domed at all, shave down any uneven parts to make the tops of the cakes flat and smooth.
Spread 1 tablespoon frosting on a cake plate or stand; this will help keep the cake in place while you decorate. Place one cake cut-side up on the plate. Dollop about 1 cup frosting on top of the cake and spread it in an even layer using a spatula, knife or spoon. Place the second cake on top of the first. Add another 2 cups frosting to the top of the cake and smooth it over the top and down the sides. Repeat with any remaining frosting until the outside of the cake is frosted and smooth. Using your hands, press the toasted coconut into the sides of the cake and sprinkle it on the top, so that the entire cake is covered in toasted coconut.
Slice and serve, or refrigerate until ready to serve. Serve at room temperature or chilled.