Line an 8” round pan with wax or parchment paper and grease the pan and the paper. Preheat oven to 350 degrees F.
To a blender or food processor, add eggs, butter, vanilla, coconut, oats, sugar, baking powder and salt. Puree until smooth, stopping to scrape down the sides if necessary. Don’t be afraid to let the mixture process for a good 3-6 minutes – you want it as smooth as possible.
Add in the corn starch and puree until smooth and combined.
Pour into prepared pan and bake for 22-25 minutes, until a toothpick comes out clean or with moist crumbs (but never batter!).
Let cool in pan for 10 minutes before turning out onto a wire rack to cool completely.
For the frosting, combine cream cheese and vanilla in a stand mixer (or use a handheld) until smooth. Add in powdered sugar, 1 cup at a time, until you reach your desired consistency.
Frost cake when completely cooled.
*Use certified gluten-free oats for a gluten-free cake