Place a strainer over a large bowl, near the stove. Put the lime zest in the bowl.

In a nonreactive saucepan, combine the eggs yolks and sugar and whisk until well blended. Stir in the lime juice, butter and salt.

Cook the mixture over medium heat, whisking constantly until the mixture is thickened. It should coat the back of wooden spoon and leave a visible trail when you run your finger through it. When the mixture has thickened and reached a temperature of 185 degrees F pour into the strainer. Press the curd through the strainer with a spatula. Stir in the lime zest.

Melt the butter in a small bowl, add 1 tablespoon of flour and stir together until it is smooth paste. With a pastry brush thoroughly coat the bottoms and sides of the three 8-inch aluminum cake pans and line them with parchment paper. If you don’t have three pans, it’s okay to bake the cakes in stages; the batter will keep at room temperature until it's needed.

The toasted coconut can be made one week ahead and stored in a plastic or glass container. Preheat the oven to 350 degrees F. Spread the sweetened coconut in a single layer on a 1/4 sheet pan. Bake the coconut for 10-15 minutes until it is golden brown. Stir and toss the coconut every 4 minutes to make sure the coconut browns evenly and doesn’t burn.

Preheat to 350°F (180°C).

Place the all-purpose flour and the coconut flour in a medium bowl and whisk to combine and remove any lumps. If you don’t have coconut flour, replace it with an equal amount of all-purpose flour.

Crack the three eggs into a bowl large enough to hold all three eggs

In the bowl of a stand mixer fitted with a paddle attachment, combine sugar, baking powder, salt, vanilla extract, butter, and virgin coconut oil. Mix on low speed to roughly incorporate, then increase to medium and beat until fluffy and light, about 5 minutes. Halfway through, pause to scrape the bowl and beater with a flexible spatula.

With the mixer still running, add eggs one at a time, letting each fully incorporate before adding the next. Scrape the sides and bottom of the bowl. Add 1/3 of the flour mixture and mix on low speed until incorporated, then add 1/3 of coconut milk and mix until just incorporated. Repeat with remaining flour and coconut milk, working in thirds as before.

Scrape bowl and beater with a flexible spatula and resume mixing on medium speed for about 5 seconds to ensure everything is well combined. The batter should look creamy and thick, registering between 65 and 68°F on a digital thermometer. (Significant deviation indicates ingredients were too warm or too cold, which can lead to textural problems with the cake.)

Fill a wide pot with at least 1 1/2 inches water, with a thick ring of crumpled tinfoil placed on the bottom to act as a "booster seat" that will prevent the bowl from touching the bottom of the pot. Place over high heat until steaming-hot, then adjust the temperature to maintain a gentle simmer. 

With mixer still running, add butter, 1 or 2 tablespoons at a time, followed by coconut oil. Initially, the volume of the meringue will decrease; it may even seem soupy along the way, but as the cool butter is added, the mixture will begin to thicken and cool. In the end, the buttercream should be thick, creamy, and soft but not runny, around 72°F (22°C). Mix in vanilla extract on low speed until well combined.

Use buttercream right away, or transfer to a large zipper-lock bag, press out the air, and seal. Buttercream can be refrigerated for up to 2 weeks and frozen for up to several months. (The main issue with longer storage in the freezer is odor absorption, not spoilage.) Rewarm to 72°F and re-whip before using.

Level the cakes with a serrated knife. Use a pastry brush to knock off any loose crumbs. Place 1 layer on a cake board or directly on a cake plate. Place the cake board or plate on a cake turntable. Place a decorating tip (Ateco #8) in a piping bag and pipe a buttercream dam around the edge of the cake. Add 3/4 cup of buttercream and spread around the center of the cake. Add 1/3 cup of the lime curd on top the buttercream and gently spread it across the to the buttercream. Add the second layer and repeat with the buttercream and lime curd. Add the third layer on top.

Cover the entire cake with a thin layer of buttercream to lock in remaining crumbs. This step is called crumb coating and will prevent crumbs from getting into the final buttercream layer. At this point you can either refrigerate the cake for 30 minutes to harden the buttercream or add your final coat of buttercream.

Coat the sides of the cake with toasted coconut. To coat the sides, take a small handful of coconut and gently press into the side of the cake. Repeat until the cake sides are thoroughly covered. Use a cake spatula to press some of the coconut along the bottom edges of the cake.

Decorate the top edge of the cake with dots or swirl. This decoration creates the dam for the lime curd. Refrigerate the cake for at least 30 minutes. Remove the cake from the refrigerate and spread the remaining lime curd across the top of the cake up to edge of your decoration.

Under a cake dome, the cake will keep for 3 days at room temperature. If the cake is refrigerated let the cake sit at room temperature at least an hour before serving.