Step 1

Cream-Cheese Frosting:Beat cream cheese with butter until fluffy, about 5 minutes. Add confectioners' sugar, 1 cup at a time, and beat until smooth, scraping down sides of bowl as necessary. Beat in vanilla and salt. Frosting can be stored in an airtight container in refrigerator for up to 5 days.

Step 2

Cake:Preheat oven to 350 degrees. Brush three 8-inch round cake pans with oil. Line bottoms with parchment rounds; brush parchment. In a bowl, whisk together flour, coconut sugar, baking powder, cinnamon, baking soda, and salt.

Step 3

In another bowl, whisk together eggs, oil, bananas, and vanilla. Stir banana mixture into flour mixture just until combined (do not overmix). Fold in pineapple, pecans, and shredded coconut. (Batter will be thick.) Divide batter evenly among prepared pans; smooth tops with a spatula.

Step 4

Bake, rotating pans halfway through, until a tester inserted in centers comes out clean, 20to 25 minutes. Transfer pans to wire racks and let cool 20 minutes; reduce oven to 325 degrees. Invert cakes onto racks; let cool completely. Meanwhile, spread coconut flakes out in a single layer on a baking sheet and toast in oven, stirring once, until golden, about 5 minutes.

Step 5

Place one cake on a cake plate, flat-side down. Spread about 3/4 cup frosting evenly across top. Place a second cake, flat-side up, on top of first layer. Spread with another 3/4 cup frosting. Place remaining cake, flat-side up, on top; spread remaining frosting evenly across top and sides of cake. Garnish with toasted coconut flakes. Refrigerate, uncovered, 30 minutes before serving. Cake can be stored, covered, in refrigerator up to 2 days; bring to room temperature before serving.