Preheat oven to 350°F. Butter and flour three 8-inch or 9-inch round cake pans or spray with baking spray, Set aside.
Cake Batter: In the large bowl of a stand mixer fitted with the paddle attachment, cream together butter, sugar and vanilla for 2-3 minutes until fully combined.
Add the eggs one at a time beating well after each addition.
In a separate bowl, use a whisk to sift together flour, baking powder, baking soda and salt.
With the mixer on low speed, add the sifted flour mixture alternately with milk, starting and ending with flour. Beat until fully combined, making sure to stop to scrape the sides of the bowl as needed. Add 1/2 cup coconut, mix well.
Divide batter evenly between pans. Bake for 25-27 minutes or until a toothpick inserted into the center comes back clean.
Make the Coconut Cream Filling: In a medium size mixing bowl, stir together sugar, fresh coconut and sour cream until fully combined. Set aside. (Reserve 1/3 of filling in an airtight container chilled to add to frosting.)
Assemble Cake Layers: Cool cake layers in pans for 20 minutes. Carefully remove first warm cake layer to a wax paper lined cake stand. Use a long skewer or a fork to poke holes all over the surface of the cake layers, then spread with 1/3 of sour cream filling.
Top with middle layer. Repeat poking holes over surface then spread with remaining 1/3 sour cream filling. (Only poke holes in TWO layers.) Place third layer on top. Let sit on the counter to cool completely, this will only take 15-20 minutes
Cover assembled cake layers with plastic wrap and chill for at least 1 day OR up to 3 days.
Coconut Cream Cheese Frosting: Use an electric mixer to beat together cream cheese, butter and reserved 1/3 coconut filling. Add 2-3 cups powdered sugar beating on medium speed until fully combined and it has a fluffy texture. You can add more confectioners' sugar if desired, to make the frosting more stiff.
Frost top and sides of the cake. Sprinkle the cake with flaked coconut gently pressing into the frosting. Chill for at least 4 hours or until frosting is set.
Slice and serve, store leftovers covered and chilled. (This cake gets better and better each day).