Preheat oven to 350 degrees F. Spray 2 9-inch round baking pans with flour-added cooking spray or grease with shortening, line with parchment and dust with flour.
Sift flour, sugar, baking powder, baking soda and salt together.
In the bowl of a stand mixer, beat the egg whites until soft peaks form. Gradually beat in ½ cup of the sugar. When thick, scrape whites into another bowl.
Add butter, shortening and sugar to the stand mixer bowl. No need to clean it. Beat for about 3 to 5 minutes or until light and creamy. Gradually beat in the egg yolks, one by one. Beat in the sour cream and the key lime juice.
Add the flour and stir or beat on medium until evenly blended. By hand, fold in the beaten egg white/sugar mixture.
Pour cake batter into cake pans and bake for 25 to 35 minutes or until a tooth pick comes out clean (mine took 32 minutes).
Cool in pans for 5 minutes and then turn cakes out onto cooling racks. Cool for 1 hour.
Spread frosting over cakes, stack and ice the whole cake with frosting. Spread toasted coconut over top and down sides. If you happen to have lemon or lime curd, you can put a layer of lemon curd between the two cake layers and on top. It really enhances the citrus flavor of the cake, but is not required.
Frosting
In a mixing bowl, beat together cream cheese and butter. Add vanilla, then add 2 cups of powdered sugar. Beat in the lime juice – beating and scraping sides of bowl all the while, then (if not sweet enough) add remaining powdered sugar ½ cup at a time until you reach desired consistency and sweetness. Adjust with more lime juice if desired.
Notes
I like a less sweet frosting, so I start with 2 cups of sugar and add more as needed. The frosting will be a bit softer without the extra sugar.