Preheat Your Oven: Preheat your oven to 350°F (175°C). Grease and flour three 9-inch round cake pans.
Mix the Dry Ingredients: In a large bowl, whisk together flour, sugar, baking soda, cinnamon, and salt.
Add the Wet Ingredients: Incorporate beaten eggs, oil, and vanilla extract into the dry mixture. Mix until well combined.
Incorporate the Fruits and Nuts: Stir in crushed pineapple with its juice, mashed bananas, and chopped pecans. Mix until evenly distributed.
Divide and Bake: Divide the batter among the prepared pans. Bake for 25-30 minutes, or until a toothpick comes out clean from the center.
Cool and Level: Cool cakes in pans on a wire rack, then remove and level the tops.
Make the Cream Cheese Frosting: Beat together softened butter, cream cheese, powdered sugar, and vanilla extract until smooth and creamy.
Assemble the Cake: Spread frosting between layers and on top and sides of the cake.
Chill and Serve: Refrigerate for 1 hour before slicing. For enhanced flavors, let the cake sit for a few hours.