Preheat oven to 350°F. Grease a 9 x 13-inch baking pan (or two 8-inch or 9-inch round cake pans).
In a medium mixing bowl, whisk together the cake flour, baking soda, salt, and cinnamon. Set aside.
Using a stand mixer fitted with a paddle attachment, combine sugar, oil, and bananas until the bananas are mashed (about 3 minutes).
Add eggs one at a time, fully incorporating after each addition. Add vanilla extract; mix to combine.
Gradually add the flour mixture until blended. Scrape down the sides and bottom of the bowl.
Beat the batter on medium speed for about 5-7 minutes.
Add crushed pineapple and chopped pecans; mix until well blended.
Pour the batter into the prepared pan. Bake in the center of the oven for 30-35 minutes (for a 9 x 13-inch pan) or 25-30 minutes (for the smaller round pans), or until a toothpick inserted in the center comes out clean.
Cool completely on a wire rack before frosting.