MAKE THE CAKE (Makes two 9-inch cake rounds)

1 Prepare the pans and preheat the oven: Heat the oven to 350F. Butter two 9-inch circular layer cake pans. Dust each pan with flour, and tap out the excess. Line the bottom of each pan with a circle of parchment paper.

2 Combine the dry ingredients: In a bowl, whisk the flour, baking powder, baking soda, and salt to blend them.

3 Separate the eggs: Place the egg yolks in one bowl and the egg whites in another. Refrigerate the egg whites until needed.

4 Make the batter: In an electric mixer with a paddle attachment, beat the butter and coconut oil on medium speed for 3 minutes. Add the sugar and beat for 2 minutes. (This beating action will aerate the cake and make it lighter.)

Switch to low speed, and beat in the eggs yolks, one at a time, mixing only until incorporated. Blend in the cream of coconut and vanilla.

With the mixer on its lowest speed, add a third of the dry ingredients (from step 2) followed by half of the buttermilk. Mix just until blended and scrape down the sides of the bowl. Add another third of the dry ingredients, followed by the remaining buttermilk. Scrape down the sides of the bowl and add the remaining third of the dry ingredients.

Remove the bowl from the mixer stand and scrape it into a large bowl.

5 Beat the egg whites: Wash out the mixing bowl with dish soap, being careful to wipe away all traces of fat. Dry thoroughly.

In the clean bowl with the whisk attachment, beat the egg whites and salt on medium high speed until stiff but not dry. They should look creamy and hold their peaks; if they start to look crumbly, stop immediately and continue with the recipe.

6 Fold the egg whites with the batter: Scoop a third of the beaten egg whites on top of the cake batter and mix gently to lighten the batter. Scoop the remaining egg whites on top of the batter and gently fold them together. (To "fold," just scoop deep into the bowl with your spatula, lift up, and gently turn the batter over on top of itself. Rotate the bowl slightly and repeat. Continue until you see no more streaks of egg white.)

7 Divide the batter evenly between the cake pans. Smooth the tops with the back of a spoon.

8 Bake the cakes: Bake for 30 to 35 minutes, or until a skewer inserted into the middle of the cake comes out clean. The baked cake should pull slightly away from the sides of the pan.

8 Cool the cakes: Set the pans on a wire rack to cool for 10 minutes. Carefully invert onto another rack, then invert again so the layers stand right-side up. Leave to cool completely. Peel off the parchment paper and assemble the cake.

Make-ahead: The cakes can be made a day or two ahead of assembly. Cool completely, wrap in aluminum foil, and refrigerate until needed.

MAKE THE LEMON CURD FILLING (Makes 1 1/4 cups)

1 Set a strainer over a bowl and place it next to the stove. Have this ready before you start the lemon curd.

2 Mix all ingredients: In a heavy bottomed medium saucepan, whisk the lemon zest, lemon juice, sugar, eggs, egg yolks, and salt. Add the butter pieces.

3 Cook the lemon curd: Set the pan on the stove over medium heat. Stirring constantly with a spatula, cook the mixture for 5 to 6 minutes, or until it thickens and comes just to a boil around the edges (170F on a thermometer).

4 Strain and cool: Quickly remove the pan from the heat and scrape the curd into the strainer. Strain, using your spatula to press the curd through the strainer. Chill in the refrigerator for 1 to 2 hours, or until cold.

Make-ahead: Once prepared, the lemon curd can be kept refrigerated for several days. (This recipe makes slightly more than you'll need; use any leftover on toast or sandwich between cookies.

MAKE THE BUTTERCREAM (Makes about 4 cups, enough for the sides and top of a 9-inch layer cake)

1 Beat the cool butter until smooth: This is a Swiss meringue buttercream, and it's incredibly creamy and light. You will be adding smooth butter to the whipped egg whites (meringue); the butter should be creamy but not too warm when you add it to the meringue.

To do this, remove the butter from the refrigerator, cut it into pieces and let stand for 10 minutes, or until slightly softened but still cool to the touch. In the bowl of a stand mixer with the paddle attachment, beat until creamy and smooth. Scrape into a separate bowl.

The butter should stay cool and smooth until needed. It should be fine at room temperature, but if your kitchen is very warm, refrigerate briefly while doing the next step and remove before the butter becomes too hard.

2 Warm the egg whites and sugar: Bring a saucepan of water to a simmer. Meanwhile, thoroughly wash the mixer bowl used for the butter in hot soapy water to remove all traces of butter and dry thoroughly.

Combine the egg whites and sugar in the mixer bowl. Set the bowl over the simmering water and whisk constantly until the mixture is very warm to the touch and the sugar is dissolved (110F). Dip your finger into the mixture and rub it against your thumb. It should feel completely smooth, not gritty.

3 Make the meringue: Set the bowl on the stand mixer and beat on medium high-speed with a whisk attachment for about 5 minutes, or until stiff peaks form. Set the speed on low and continue to beat the meringue for 15 minutes longer, or until cool.

4 Add the butter: On low speed, beat in butter, a heaping tablespoon at a time, until it is all incorporated and the buttercream is smooth. Beat in the vanilla extract.

If the mixture looks slightly grainy or curdled, it may be that the butter is too cool. Simply set the bowl of buttercream over simmering water for a few seconds to warm it. If the buttercream becomes soupy, it is probably too warm. Chill for 20 minutes or so, and try mixing again.

Make-ahead: You can refrigerate this buttercream for up to 3 days. Allow it to come to room temperature and beat with a paddle attachment to bring it to spreading consistency. If necessary, warm it carefully over simmering water.

ASSEMBLE THE CAKE

1 Toast the coconut: Heat the oven to 350°F. On a baking sheet, spread the coconut flakes (not the shredded coconut). Bake for 3 to 4 minutes, or until the coconut is golden. Watch carefully, since it burns easily. Cool on the baking sheet.

2 Prepare the cake for decorating: Cut 4 parchment paper strips that are about 3 inches wide. If the cake has domed in the oven, shave off the domed peaks with a serrated knife to make the layers flat and even.

On a flat surface or a flat cake stand, place the bottom layer, trimmed side down. Slip the parchment strips partially under the cake. Brush off any excess crumbs.

3 Spread 1 cup of lemon curd on top of the cake. Place the second layer on top, trimmed side down. (You will have leftover lemon curd; this will keep in the fridge for at least a week and can be spread on toast or sandwiched between cookies.)

4 Spread a "crumb coating" of frosting over the cake: Spread about 1/3 of the buttercream on top and around the sides of the cake in a thin coating. Refrigerate for 20 minutes, or until the buttercream is firm. This step helps to both minimize crumbs and to firm up the lemon curd so that it does not ooze into the icing.

5 Frost the cake and coat with coconut: Spread the remainder of the buttercream over the top and sides of the cake. With a cupped hand and the aid of a spatula, cover the cake with the shredded coconut.

6 Finish the cake: Remove the strips of parchment from under the cake and brush off the coconut that is around the bottom of the cake. Decorate the top with the toasted coconut flakes.