a large piping bag fitted with a large star tip; a small piping bag
For the coconut sponge cake: Preheat the oven to 375 degrees F. Coat an 11-by-17-inch rimmed baking sheet or jelly roll pan with cooking spray; line the bottom with parchment and spray the parchment.
Add the egg whites and lemon juice to a stand mixer fitted with the whisk attachment. Beat on medium speed until soft peaks form, about 3 minutes. Add 1/2 cup of the confectioners' sugar and increase the speed to medium high; beat until stiff peaks form, 3 to 4 minutes.
Whisk the egg yolks together with the milk, vegetable oil and coconut extract in a separate large bowl until smooth. Sift the flour, baking powder, salt and remaining 1 cup confectioners' sugar together into a medium bowl; whisk into the yolk mixture until smooth. Stir about a third of the whites into the batter with a rubber spatula, then fold in the remaining whites in 2 batches.
Spread the batter in the prepared pan. Bake until a toothpick inserted in the center comes out clean but the cake is still pale, 12 to 14 minutes.
Immediately sift confectioners' sugar generously over the top of the warm cake and loosen the edges with a knife; lay a clean kitchen towel (not terry cloth) over the cake. Place another baking sheet over the towel and flip the baking sheets to invert the cake onto the towel. Remove the top baking sheet and parchment. Starting at a short end, roll up the cake and towel together into a spiral. Transfer seam-side down to a rack and let cool completely, about 1 hour.
For the frosting and cream: Add the butter and salt to a stand mixer fitted with the paddle attachment. Beat on medium speed until smooth and fluffy, about 1 minute. Gradually beat in the confectioners' sugar until smooth. Add the coconut cream and beat on medium-high speed until thick, about 2 minutes. Transfer 2 cups of the frosting to a large piping bag fitted with a large star tip. Set aside.
Add the toasted coconut flakes, chopped cherries and maraschino cherry liquid to the remaining frosting in the mixer and mix on low speed until combined. Transfer 1/2 cup of the maraschino cream to a small piping bag.
Dry the cored pineapples with paper towels. Stand them upright on a baking sheet and pipe the maraschino cream into the center of each. Tap each pineapple on the baking sheet to pack in the cream, then pipe in more to fill.
Gently unroll the cake. Spread the remaining maraschino cream over the cake, leaving about a 1/4-inch border. Arrange the pineapples end to end in a row in the middle of the cake, lining up the cores. Bring the ends of the cake up and together around the pineapples. Trim any cake that is overlapping so the ends just meet. Trim the short ends with a serrated knife to create a clean edge. Turn the cake seam-side down.
Pipe the white frosting on top of the cake to decorate and garnish with the toasted coconut chips, dried pineapple rings and maraschino cherries.
When measuring flour, we spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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