Preheat the oven to 350°F (175°C). Grease and flour three 9-inch round cake pans.

In a large mixing bowl, sift together the all-purpose flour, granulated sugar, baking soda, ground cinnamon, and salt.

In a separate bowl, combine the beaten eggs and vegetable oil. Incorporate the wet mixture into the dry ingredients, stirring only until the flour is just moistened.

Fold in the vanilla extract, crushed pineapple with its juice, toasted pecans, and mashed bananas until evenly distributed throughout the batter.

Distribute the batter evenly across the three prepared cake pans to ensure uniform baking.

Bake in the center of the oven for 25 to 30 minutes, or until a cake tester inserted into the center of the cakes emerges clean.

Allow the cakes to cool in the pans for 10 minutes before transferring them to wire racks to cool completely to room temperature.

Prepare the frosting by beating the softened cream cheese and butter in a stand mixer until smooth and aerated.

Gradually incorporate the powdered sugar and the remaining vanilla extract, beating at medium speed until the frosting is light and fluffy.

Assemble the cake by applying a layer of frosting between each cake round, then frost the top and exterior sides of the tiered structure.