Adjust oven rack to middle position and heat oven to 350°F.
Grease 2 light-colored 9-inch round cake pans, line with parchment paper, grease parchment, and flour pans.
Drain pineapple in fine-mesh strainer set over bowl, pressing to remove juice. Pour juice into small saucepan and cook over medium heat until reduced to 1/3 cup, about 5 minutes; set aside.
Whisk flour, baking powder, baking soda, cinnamon, and salt together in bowl.
Whisk sugar and eggs together in separate large bowl; whisk in oil.
Stir in bananas, pecans, vanilla, drained pineapple, and reduced pineapple juice.
Stir in flour mixture until just combined.
Divide batter evenly between prepared pans and smooth tops with rubber spatula.
Bake until dark golden brown on top and toothpick inserted in center comes out clean, 50 to 55 minutes (mine was ready in 45 minutes), rotating pans halfway through baking.
Let cakes cool in pans on wire rack for 20 minutes.
Remove cakes from pans, discarding parchment, and let cool completely on rack, about 2 hours.