In a large bowl, mash the bananas. Stir in the crushed pineapple, oil, vanilla extract, eggs, brown sugar, and sugar until everything is well combined. In a separate medium bowl, stir together the flour, cinnamon, salt, baking soda, ginger, allspice, and chopped pecans. Gently fold the dry ingredients into the wet ingredients until everything is well combined. Spread the batter evenly into the prepared cake pans. Bake for 30-32 minutes, or until a toothpick comes out with just a few crumbs clinging to it. Let the cakes cool completely before frosting.
In a large bowl, beat together the cream cheese and butter until smooth. Slowly beat in the powdered sugar and cornstarch until you have a thick mixture. Stir in the vanilla extract and salt. Optionally, trim the cake layers to create flat layers, and frost the cake as desired.