1. Preheat oven to 350 degrees F. Generously butter and flour 2- 8 inch cake pans, or 1 sheet pan. Blend the cake wet ingredients and the dry ingredients separately, then combine. Fold in coconut. Pour into cake pan(s). Bake for 30-35 minutes (or until a toothpick comes out clean). Cool completely before proceeding. Put a metal mixing bowl into the fridge for 30 minutes to cool.
2. If using sheet pan, cut cake in half to make layers. Put the first layer down on a cake plate, then poke full of holes with a chopstick. The frosting is a bit runny, so the holes let the frosting seep down into the cake.
3. For frosting, open the can of coconut milk, which should be almost entirely solid. Pour off any of the milk that didn't solidify (I use my leftover for coffee that afternoon), then put the solids into the mixing bowl. Using the whisk attachment on mixer (or whisk by hand), beat until well combined (about 20 seconds on high). Then, add 1-2 cups powdered sugar (to taste, really).
4. Beat the sugar into the coconut cream (no more than 30 seconds). Pay attention to these times! The milk tends to liquefy if you go too long. ( This "frosting" isn't as solid as buttercream. I have seen similar recipes presented as whipped cream, so expect that kind consistency.) Spread a generous amount of the frosting on top of the bottom cake layer. Then, put the top layer on top. Poke that second layer full of holes, and frost the top and sides with the remainder of the frosting.
5. Cover the whole thing with shredded coconut. I like the unsweetened kind, but I'm sure the sweetened works just as well, especially if you don't add as much sugar to the frosting. Unless you eat the whole cake in one go right after you finish frosting it , you need to keep it cold in the refrigerator so the coconut frosting doesn't turn into coconut milk again.
Enjoy!
Source of recipe: I wrote this recipe after my mother raved about Paula Dean's (very non-vegan) coconut cake.