How to Make It
Preheat the oven to 350°. Brush a 9-by-13-inch baking dish with butter. In a stand mixer fitted with the paddle, beat the egg yolks with the granulated sugar at high speed until light and fluffy, about 5 minutes. Scrape into a large bowl. Clean the mixer bowl.
In the stand mixer fitted with the whisk, beat the egg whites at high speed until medium peaks form, about 1 minute. Using a rubber spatula, stir a large scoop of the egg whites into the egg yolk mixture to lighten it. Gently fold the remaining whites into the egg yolk mixture until no white streaks remain.
Sift the flour over the egg mixture, then gently fold together until just combined. Scrape the batter into the prepared baking dish and smooth the top. Bake for about 15 minutes, until springy and light golden. Let cool. Leave the oven on.
Meanwhile, spread the coconut on a small rimmed baking sheet and toast in the oven, stirring halfway through, for about 5 minutes, until golden. Let cool.
Using a bamboo skewer or a fork, poke holes all over the cooled cake. In a medium bowl, whisk the condensed milk with the evaporated milk, whole milk, rum and vanilla. Pour the milk mixture evenly over the cake. Cover the baking dish with plastic wrap and refrigerate until the cake is evenly moist, at least 3 hours.
In a medium bowl, whisk the cream with the confectioners’ sugar until medium peaks form. Dollop the whipped cream on the cake and spread it in an even layer. Sprinkle the toasted coconut over the top. Dust the cake with cinnamon and cut into squares. Serve, spooning some of the milk mixture from the baking dish onto each plate.