Preheat the oven to 350°F. Grease and flour two 9-inch round cake pans, tapping out any excess flour.
In a large mixing bowl, whisk together the flour, sugar, baking soda, cinnamon, and salt until evenly combined.
Add the eggs, vegetable oil, and vanilla extract to the dry ingredients. Stir until just combined, then fold in the crushed pineapple, mashed bananas, and chopped pecans. The batter should be thick and lumpy.
Divide the batter evenly between the prepared cake pans. Bake for 25 to 30 minutes, or until a toothpick inserted into the center comes out clean. Let the cakes cool in the pans for 10 minutes, then transfer to a wire rack to cool completely.
While the cakes cool, make the frosting. In a large bowl, beat the softened cream cheese and butter with an electric mixer on medium speed until smooth and creamy, about 2 minutes. Gradually add the powdered sugar, 1 cup at a time, beating well after each addition. Mix in the vanilla extract until the frosting is fluffy and smooth.
Once the cakes are completely cooled, spread a layer of frosting on top of one cake layer. Place the second layer on top and frost the top and sides of the entire cake.
Notes
Let the cakes cool completely before frosting to prevent the frosting from melting.