Preheat your oven to 350°F. In a large bowl, whisk together the flour, sugar, salt, baking soda, and cinnamon. Add the eggs and vegetable oil, stirring gently until the dry ingredients are just moistened. Mix in the vanilla extract, pineapple (with juice), bananas, and toasted chopped pecans until evenly combined.

Grease three 9-inch round cake pans with vegetable shortening, then dust them with flour. Divide the batter evenly among the prepared pans.

Place the pans in the preheated oven and bake for 25 to 30 minutes, or until a wooden toothpick inserted into the center comes out clean. Allow the cakes to cool in the pans on wire racks for 10 minutes, then remove from pans and let them cool completely on the racks, approximately 1 hour.

In a mixing bowl, beat the softened cream cheese and butter on medium-low speed until smooth and creamy. Gradually incorporate the powdered sugar, mixing at low speed until each addition is fully blended. Stir in the vanilla extract, then increase the mixer speed to medium-high and beat until the frosting is light and fluffy, 1 to 2 minutes.

Position the first cake layer on a serving platter and spread 1 cup of frosting evenly across the top. Add the second layer and spread with another 1 cup of frosting. Place the third layer on top, then use the remaining frosting to coat the top and sides of the entire cake.

Arrange the toasted pecan halves on the top of the cake in a circular design, or in a pattern of your choice, to garnish.