Instructions

for the soak

Whisk 2/3 cup canned coconut milk and 3 tablespoons confectioners’ sugar in small bowl until sugar is dissolved; set aside.

for the cake

Adjust oven rack to middle position and heat oven to 350 degrees. Grease three 8-inch round cake pans, line with parchment paper, and grease parchment. Whisk 2¼ cups (11¼ ounces/319 grams) all-purpose flour, 1½ cups (4½ ounces/129 grams) sweetened shredded coconut, 2 teaspoons baking powder, and ¾ teaspoon table salt together in bowl. Whisk 1 cup buttermilk and ½ cup vegetable oil together in liquid measuring cup.
Using stand mixer fitted with paddle attachment, beat 12 tablespoons softened unsalted butter and 1¾ cups (12¼ ounces/347 grams) granulated sugar on low speed until smooth, about 1 minute. Increase speed to medium-high and beat until pale and fluffy, 1 to 2 minutes. With mixer running, add 4 large eggs, one at a time, and beat until combined. Continue to beat until mixture is pale, thick, and smooth, 1 to 2 minutes longer, scraping down bowl as needed.
Turn off mixer. Add half of flour mixture and mix on low speed until just incorporated, about 30 seconds. With mixer running, stream in buttermilk mixture and mix until just incorporated, about 30 seconds. Add remaining flour mixture and mix until just incorporated, about 30 seconds. Divide batter evenly among prepared pans and smooth tops with silicone spatula. Tap pans firmly on counter to release any large air bubbles.
Bake until cakes are golden and toothpick inserted in centers comes out clean, 18 to 22 minutes, rotating pans halfway through baking. Let cakes cool in pans on wire racks for 15 minutes. Invert cakes onto racks, discarding parchment. Using pastry brush, gently dab soak onto layers until evenly moistened, about ¼ cup per layer. Let layers cool completely on racks, about 2 hours.

for the frosting

Combine 1 cup room temperature heavy cream, ¾ cup room-temperature canned coconut milk, and 2½ teaspoons coconut extract in clean liquid measuring cup. In clean stand mixer fitted with whisk attachment, beat 30 tablespoons (3¾ sticks) cut and softened unsalted butter and 1 teaspoon table salt on medium-high speed until smooth, about 1 minute. Add 3¾ cups (15 ounces/425 grams) confectioners’ sugar and beat on low speed until incorporated, about 1 minute. Increase speed to medium-high and whip until mixture is light, fluffy, and nearly doubled in volume, 4 to 5 minutes, scraping down bowl as needed.
With mixer running on medium-low speed, slowly stream in cream mixture until fully incorporated, about 2 minutes, scraping down bowl halfway through streaming (mixture will appear curdled; this is OK).
Turn off mixer and scrape down bowl. Whip mixture on medium-high speed until frosting is fluffy and creamy, about 2 minutes. Remove bowl from mixer. Using silicone spatula, gently fold frosting to smooth any large air bubbles or lumps. (Frosting can be refrigerated for up to 4 days; let soften at room temperature, about 1 hour, then rewhip on medium speed until smooth and fluffy, about 1 minute.)
To assemble cake, place 1 cake layer on cake platter, soaked side up. Spread 1¼ cups frosting evenly over top, to edges of cake. Repeat with remaining layers, spreading 1¼ cups frosting evenly over each. Using offset spatula and bench scraper, smooth remaining frosting evenly over sides of cake, then smooth top. Gently press 2 cups (6 ounces/170 grams) toasted sweetened shredded coconut onto sides and top of cake. Serve. (Cake can be refrigerated for up to 2 days; let cake come to room temperature before serving.)