Step 1

To make the cake, heat the oven to 350°F with racks in the upper- and lower-middle positions. Mist four 8-inch round cake pans with cooking spray. Line the bottoms with rounds of kitchen parchment, then mist the parchment. Dust the pans with flour, then knock out the excess.

Step 2

In a medium bowl, whisk together the flour, baking powder, baking soda and salt. In another medium bowl or a 1-quart liquid measuring cup, whisk together the eggs, buttermilk and vanilla; set aside.

Step 3

In a stand mixer with the paddle attachment, beat the butter and white sugar on medium until light and fluffy, 4 to 5 minutes. With the mixer running on low, add about one-third of the flour mixture followed by about half of the egg mixture. Next, add about half of the remaining flour mixture, then the remaining egg mixture and finally the remaining flour mixture; scrape the bowl as needed. After the final addition, increase to medium and beat until well combined, about 1 minute. Fold the batter with the spatula, scraping along the bottom and sides of the bowl to ensure no pockets of flour remain; the batter will be thick.

Step 4

Divide the batter evenly among the prepared pans, then spread in an even layer and smooth the surface. Gently rap each pan against the counter to remove any air bubbles. Place 2 pans on the upper rack and 2 on the lower, spacing them evenly. Bake for 15 minutes, then quickly move the 2 pans on the upper rack to the lower rack and the pans on the lower rack to the upper rack. Bake until the center of the cakes spring back when touched and a toothpick inserted at the center comes out clean, 10 to 12 minutes. Let the cakes cool in the pans on wire racks for about 15 minutes.

Step 5

Run a paring knife around the edge of each pan to loosen the cakes. One at a time, invert the cakes onto the racks and lift off the pans. Peel off and discard the parchment, then cool the cakes to room temperature.

Step 6

To make the frosting, in a stand mixer with the paddle attachment, beat the butter on medium until smooth and creamy, about 1 minute. With the mixer running on low, add about one-third of the powdered sugar and beat until fully incorporated, 2 to 3 minutes, scraping the bowl as needed. Gradually add the remaining powdered sugar; continue beating until smooth and creamy, about 2 minutes. Add the half-and-half and vanilla; beat on low until combined and the frosting is smooth, about 1 minute, scraping the bowl as needed. Increase to medium and beat for 1 minute to aerate slightly.

Step 7

To assemble the cake, if the layers domed in the center during baking, turn them upright. Using a long-bladed serrated knife held parallel to the counter and a sawing motion, carefully trim off the domes. (If the cakes baked up flat, there is no need to trim them.)

Step 8

Set 1 cake layer on the center of a cake plate. (If desired, to keep the plate clean as you frost the cake, cut 5 kitchen parchment strips, each measuring roughly 6 by 3 inches, and tuck them under the edges of the bottom cake layer so they cover the plate). Scoop about ¾ cup frosting onto the center of the cake and, using an icing spatula, spread in an even layer to the edges of the cake. Sprinkle about 2 tablespoons coconut evenly over the frosting. Place a second cake layer on top, aligning it with the bottom layer, then frost in the same way and sprinkle with 2 tablespoons of the remaining coconut. Repeat with the third layer. Place the final cake layer, bottom side up, on top. Spread the remaining frosting onto the top and sides of the cake. (Remove and discard the parchment strips, if used.)

Step 9

Add the remaining coconut to a medium bowl and toss with your hands to separate the shreds. Pick up a handful and gently press it against the side of the cake; repeat until the sides are completely coated. Return any coconut that falls off to the bowl, then sprinkle it over the top of the cake to cover.