Prep for making pineapple flowers: Preheat oven to 225°F. Line 2 rimmed baking sheets with Silpats or parchment. Peel pineapples and use a small melon baller to remove and discard any "eyes."

Make dried pineapple flowers: Slice pineapple very thinly; place slices on baking sheets. Cook until tops look dried, about 30 minutes. Flip slices; cook until completely dried, 25 to 30 minutes more. Cool on a wire rack.

Preheat oven and prep pans: Increase heat to 350°F, with rack in the center. Butter two 9-by-2-inch round cake pans. Line the bottoms of the pans with parchment paper. Butter paper, and dust the pans with flour, tapping out any excess. Set aside.

Mix dry ingredients: In a medium bowl, sift together flour, baking soda, cinnamon, and salt; set aside.

Combine oil, vanilla, and sugar; add eggs one at a time: In the bowl of an electric mixer, beat oil, vanilla, and sugar until combined, about 2 minutes. Add eggs one at a time, incorporating each before adding the next. Beat at medium speed until mixture is pale yellow and fluffy, about 3 minutes.

Combine banana, pineapple, walnuts, and coconut: In a medium bowl, mix together banana, pineapple, walnuts, and coconut.

Add banana mixture to egg; blend in dry ingredients: Add to egg mixture; stir until well combined. Add flour mixture; blend well.

Divide batter between pans and bake: Divide batter between pans. Bake, rotating pans halfway through, until golden brown and a cake tester inserted in the center comes out clean, 30 to 40 minutes.

Cool: Transfer pans to a wire rack. Let cool 15 minutes. Run a knife around edges to loosen. Invert onto racks; reinvert, top side up. Cool completely.

Assemble cake: With a serrated knife, trim and discard rounded top off one layer. Place layer on serving platter. Using an offset spatula, spread top of layer with ¼ inch of frosting. Top with untrimmed layer.

Frost and decorate: Frost sides and top of cake with remaining frosting. Decorate with pineapple flowers, if desired. Serve at room temperature.