Game Plan: Start boiling the water when you turn the oven on so it's ready when the cake goes into the oven. Separate eggs while the lime concentrate thaws in the microwave.
Position a rack in the center of the oven and preheat to 325 degrees F. Lightly butter a 1-quart gratin dish or 8-inch round cake pan and set it in a roasting pan.
Beat the 2 tablespoons butter with 1/2 cup sugar in a large bowl until creamy, using a handheld electric mixer. Beat in the flour, then the egg yolks, limeade concentrate, coconut milk, and salt. (For the airiest egg whites, clean the beaters thoroughly so none of this mixture is left on them.) In another medium bowl whip the egg whites until they form soft peaks. While whipping, slowly pour in the remaining 1/4 cup granulated sugar and continue beating until the whites hold stiff, glossy peaks. Fold a quarter of the whites into the coconut-lime mixture, then fold in the remaining whites.
Pour the batter into the prepared baking dish and add enough boiling water to the roasting pan to come halfway up the side of the dish. Bake about 35 minutes or until the top of the pudding cake is slightly puffed and golden. Remove from the water bath and cool on a wire rack for 10 minutes; serve warm. Garnish each serving with toasted coconut, if desired.
Baking the cake in a water bath ensures that it will bake evenly and retain its luscious, saucy bottom.
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