Whisk together the flour, corn starch, salt, baking powder, baking soda, and coconut shreds until completely combined and set it to the side.
Next, cream together the butter and sugar in a stand mixer with the paddle attachment on medium-high speed until light and fluffy, which takes about 5 to 7 minutes.
Add in the coconut extract to the mixer and then add in 1 egg white at a time until it is completely mixed in.
Pour in the oil. Stop and scrape the bowl.
Alternate adding in the dry ingredients with the 1 cup of liquid only from the canned coconut milk beginning with dry and ending with dry until mixed in on low speed. You should be adding the dry in 3 batches and the wet in 2 batches.
Distribute the batter evenly between three 9” cake pans with parchment paper that have also been greased with butter. Bake at 350° for 27 to 29 minutes or until lightly browned, firm in the center, and when sticking a toothpick in the center it comes out clean.
Cool completely on a rack, which takes about 90 minutes to 2 hours.
With about 15 to 30 minutes left in the cake cooling process, make the buttercream recipe.
Whip together the softened butter, cream cheese, and coconut cream leftover from the can to a stand mixer with the paddle attachment and whip on high speed for 5 to 7 minutes or until creamy and smooth.
Pour in the coconut extract then add in 1 cup of powdered sugar at a time on low to medium speed until mixed in and completely smooth.
Ice the cake in layers until it is completely coated.
Cover the cake entirely on all sides with toasted coconut.
Slice and serve.
Notes
Make-Ahead: You can make this cake up to 1 day ahead of time.How to Store: Cover and keep at room temperature for up to 3 days. Place it in the refrigerator and cover it for up to 5 days. You can freeze this covered for up to 3 months and thaw it in the refrigerator for 1 day before serving.How to Serve: Pull the cake out of the refrigerator and let it sit for 1 hour at room temperature before serving.If you have cake flour on hand, replace the all-purpose flour and cornstarch in this recipe with 3 ¾ cups and 3 tablespoons of cake flour.Do not use coconut milk from the carton in the milk section of the grocery store. That will not work.I highly recommend sprinkling additional toasted coconut to each slice when serving.Try using the leftover egg yolks in my pasta carbonara.