Preheat the oven to 350 degrees F (180 degrees C).
Grease three 8-inch cake pans or two 9-inch cake pans and set aside.
Put Carrot (3 cup) and Pineapple (1 cup) in a food processor and pulse on low until carrots are rice-sized.
Using a standing mixer with a paddle attachment, mixed processed carrots, pineapple, Egg (5), Granulated Sugar (1 cup), Brown Sugar (1 cup), Vegetable Oil (1 1/3 cup), Vanilla Extract (1 teaspoon), and Coconut Extract (2 teaspoon) until combined.
Mix the All-Purpose Flour (3 cup), Salt (1 teaspoon), Baking Soda (1 tablespoon), and Ground Cinnamon (2 teaspoon) together and add to the wet mixture.
Mix together for one minute and pour the batter evenly into the prepared cake pans.
Bake on the middle rack of the preheated oven for 40-45 minutes (for three 8-inch pans) or until a toothpick comes out clean from the center. Or, for 50-55 minutes for two 9-inch cake pans.
Let the cake cool in the pans for at least 10-15 minutes before removing and cooling on a rack. Be careful when removing, as it's a delicate cake.
Make the frosting. In a standing mixer with the whisk attachment on high speed, whip Unsalted Butter (2 cup), Coconut Extract (2 teaspoon) and another pinch of salt together until the color becomes pale, about 5 minutes.
Scrape down the sides of the bowl. Reduce mixer speed to medium, and slowly drizzle the Sweetened Condensed Milk (1 can) into the butter. Whip for another minute.
Add the Powdered Confectioners Sugar (1 1/2 cup). Whip mixture again until smooth and combined.
Layer the frosting with the cooled cakes and sprinkle the top with Unsweetened Coconut Flakes (1/2 cup).