Preparation

Make the cake

• Position a rack in the center of the oven, and heat the oven to 350°F. Grease a 13x9x2-inch pan with softened butter. Line with parchment and set aside.
• In the bowl of a stand mixer fitted with the paddle attachment (or in a large bowl with a handheld electric mixer), combine the flour, sugar, baking powder, and salt. Mix on low speed to combine. Add the butter, and mix until the butter is coated in flour and resembles coarse meal.
• Add the extracts and then the eggs and yolks, one at a time, mixing until combined. Add the coconut cream and then the milk, and increase the speed to medium. Beat until the batter is smooth and glossy, about 30 seconds. Fold in the shredded coconut by hand with a silicone spatula.
• Transfer the batter to the prepared pan, scraping the mixer bowl well. Bake, rotating the cake halfway through, until a cake tester comes out clean or with a moist crumb or two, 30 to 35 minutes.
• Let cool in the pan on a rack for about 10 minutes. Carefully invert the cake onto the rack, then flip right side up to cool completely.

Make the buttercream

• In the bowl of a stand mixer fitted with the paddle attachment (or in a large bowl with a hand-held electric mixer), beat the butter on medium-low speed until smooth and light in color, about 3 minutes.
• Add the sugar a cup at a time, alternating with the coconut cream and making sure that each addition is fully incorporated. Scrape the bowl with a silicone spatula as needed.
• Add the extract and salt, and continue beating on medium speed for 5 to 10 minutes. The frosting will be light, creamy, and fluffy.
  Generously spread the cooled cake with the frosting in decorative swoops, then sprinkle with the toasted coconut.
• Store the cake lightly wrapped in plastic wrap at room temperature for up to 3 days.