• Grease 3, 8-inch cake pans and dust with flour. Heat oven to 350 degrees.
• Whisk together flour, salt and baking powder in a bowl and reserve. Place butter and sugar in the bowl of a standing mixer fitted with paddle attachment and beat until fluffy, about 2 to 3 minutes. Add 3 egg yolks, 1 at a time, beating after each addition and scraping down sides of bowl with spatula. Lower speed and gradually add flour mixture. Batter will be thick and pasty.
• Whisk together cream of coconut, coconut milk, rum and orange juice. Alternately add shredded coconut and the orange juice mixture to the batter.
• In the clean bowl of a standing mixer fitted with the whisk attachment, whip 6 egg whites until soft peaks form. Gently fold into batter.
• Divide batter evenly among prepared pans. Bake for 45 to 60 minutes. Cool in pans on wire rack. Unmold cakes once cool.

Make the Frosting

• In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and cream cheese. Add vanilla extract. Gradually add confectioners’ sugar, scraping down sides of the bowl with a rubber spatula. Mix until combined and fluffy.
• Spread ¼-inch-thick layer of frosting on top of the first layer of cake. Sprinkle with toasted coconut. Place next cake layer on top and repeat with frosting and coconut. Repeat with the third layer, spreading frosting on top and around sides of cake. Hold cake steadily in one hand and use other hand to pat remaining coconut onto edges of cake.