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For the cake:
3 cups cake flour
1 Tbs. baking powder
1/2 tsp. kosher salt
8 oz. salted butter, room temperature
2 cups sugar
4 eggs, room temperature
1½ cups whole milk
1 tsp. pure vanilla extract
1 can sweetened condensed milk
For the frosting:
16 oz. cream cheese, room temperature
4 oz. salted butter, softened
4 tsp. pure vanilla extract
2 dashes kosher salt
2 (10-oz.) boxes powdered sugar
8 cups sweetened flaked coconut
Preheat oven to 350°F. Grease and flour three 10-inch cake pans.
Sift the flour, baking powder, and salt together into a bowl. Put the butter and sugar in the bowl of a stand mixer with the paddle attachment and beat on medium speed until light and fluffy, three to four minutes. Add the eggs one at a time, mixing well after each addition and scraping down the sides of the bowl after each.
Combine one cup of the whole milk with the vanilla extract. Set the mixer’s speed on low and alternate adding the dry ingredients and milk mixture, beginning and ending with the flour. Beat until all are mixed in well. Divide the mixture between the prepared cake pans. Bake at 350°F for 40 minutes, or until set and a toothpick inserted into the center of each layer comes out clean.
Put the pans on wire racks and let the layers cool for 10 to 15 minutes. Invert the layers onto parchment paper. Mix the condensed milk and the remaining half-cup of whole milk in a bowl. Poke holes in each layer and pour the milk mixture into each layer. This gives the cake additional moisture. The layers will be damp, so use a long cake spatula when stacking them so that they do not break.
Put the cream cheese, butter, vanilla, and salt in the bowl of a stand mixer with the paddle attachment and mix until smooth. Gradually add the powdered sugar and mix until all the ingredients are combined and smooth. Using a rubber spatula, fold in four cups of coconut.
Using a long cake spatula, place one layer on a cake stand and frost the top of that layer. Repeat for layers two and three. Once all three layers are stacked and frosted, frost the outside of the cake. When finished, use the remaining four cups of coconut to pat on the sides and top. Refrigerate after one day. In a closed cake carrier, the cake will keep for up to five days in the refrigerator.