Step 1

Preheat oven to 350 degrees, 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.

Step 2

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

Step 3

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.

Step 4

In a medium bowl, mix together banana, pineapple, walnuts, and coconut. Add to egg mixture; stir until well combined. Add flour mixture; blend well.

Step 5

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.

Step 6

Transfer pans to a greased wire rack. Let cool 15 minutes. Run a knife around edges to loosen. Invert onto racks; reinvert, top side up. Cool completely. Assemble cake, or wrap each layer well and freeze (thaw before using).

Step 7

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 1/4 inch of frosting. Top with untrimmed layer. Frost sides and top of cake with remaining frosting. Decorate with pineapple flowers, if desired. Serve at room temperature. (Cake can be refrigerated up to 3 days.)