Cake:
6 large eggs, at room temperature
1⅓ cups (181 grams) all-purpose flour
1 tsp. baking powder
¼ tsp. fine sea salt
½ stick (4 Tbsp.) unsalted butter, melted
1 cup (200 grams) sugar
Coating:
About 2 cups (160 grams) shredded unsweetened coconut
For the chocolate sauce
1 Tbsp. plus 1 tsp. unsalted butter
½ cup water
2¼ cups (254 grams) confectioners’ sugar
3½ Tbsp. unsweetened cocoa
To make the cake:
At least one day before serving, center a rack in the oven and preheat it to 350°F. Butter a 9-inch square cake pan and dust with flour, or use baker’s spray. Line the bottom of the pan with parchment paper. Have a sifter or strainer at hand.
If your eggs are still cool to the touch, put them in a bowl of hot water for 5 minutes—warmed eggs beat more voluminously than cold eggs and you want volume.
Whisk the flour, baking powder and salt together. Put the melted butter in a small bowl.
Working in the bowl of a stand mixer fitted with a whisk attachment, or in a large bowl with a hand mixer, beat the sugar and eggs together on medium-high speed until they triple in volume, about 4 minutes; when you lift the whisk, the batter should form a ribbon as it falls into the bowl. If you’re using a stand mixer, remove the bowl. Grab a big flexible spatula, sift or strain one third of the flour mixture over the eggs and sugar and gently fold it in. Repeat twice more, until all of the flour is in. No matter how gentle you are, the batter will deflate—it’s the nature of the cake.
Stir two or three spoonfuls of the batter into the melted butter and then gradually fold the butter mixture into the batter in the bowl. As you fold, check the bottom of the bowl—the butter has a tendency to lurk there: Find it and fold it in. Scrape the batter into the pan and jiggle the pan to level it.
Bake for 26 to 29 minutes, or until the cake is golden, is starting to come away from the sides of the pan and springs back when gently prodded; a tester inserted into the center of the cake will come out clean. Transfer the pan to a rack and wait for 5 minutes, then run a table knife around the edges of the pan to loosen the cake. Unmold the cake onto the rack, carefully peel away the paper and let cool to room temperature. Lightly cover the cake—you can put a kitchen towel over it—and leave it out overnight. (The cake can be wrapped in plastic and kept at room temperature for up to 2 days.)
To cut the cake and get ready to finish it: Unwrap the cake if necessary and place it right side up on a cutting board. The top will have crowned in baking, so use a long serrated knife and a gentle sawing motion to level the cake. Cut the cake into 16 squares, each about 2¼ inches on a side. Place the cubes on a rack set over a piece of parchment or a baking sheet—the sauce will drip—and prepare your dipping and coating station: Put some of the coconut in a shallow bowl—work with a little at a time, so that if you get chocolate sauce in it (almost inevitable), you’ve got backup. Have four table forks at hand—two for dipping and two for turning the chocolate-coated cake cubes in the coconut.
To make the sauce:
Bring the butter and water to a boil in the microwave. Sift or strain the confectioners’ sugar and cocoa together into a bowl—a deep narrow one is best. Pour the boiling water–butter mixture into the bowl and stir with a flexible spatula to blend.
To dip and coat the cake: One by one, drop the cubes of cake into the sauce, turning each one around with two forks until it’s coated on all sides. Lift up the cube, letting any excess sauce drip back into the bowl, and return the cube to the rack. After you’ve dipped two or three cubes, one by one, coat each of the dipped cubes with coconut, using two clean forks to turn the cubes around in the coconut. Continue working in batches until all of the cubes are dipped and coated. If the sauce thickens as you work, thin it with drops of very hot tap or boiling water.
Leave the Lamingtons on the rack to set for an hour or so before serving.
You can wrap the Lamingtons well and keep them at room temperature for 3 days or so. Yes, they’ll be drier, but they’ll still be so good.