Heat the oven to 350 degrees.
Grease and parchment-line three 9-inch round pans.
Whisk the flour, sugar, baking soda, salt, and cinnamon in a large bowl.
In a separate bowl, whisk the eggs, oil, and vanilla until smooth.
Stir the crushed pineapple and mashed bananas into the wet mixture.
Pour the wet ingredients into the dry ingredients.
Fold gently until almost combined.
Add the chopped pecans.
Fold again just until no dry flour remains.
Divide the batter evenly among the three pans.
Bake for 25 to 30 minutes.
Cool the layers in the pans for 15 minutes.
Turn the layers onto wire racks and cool completely.
Beat the cream cheese and butter together until smooth.
Add the powdered sugar gradually, then add the vanilla.
Beat until the frosting is smooth and thick.
Add 1 to 2 tablespoons milk only if the frosting needs a little loosening.
Set one layer on your plate or cake stand.
Spread frosting across the top.
Repeat with the second layer.
Add the third layer with the flattest side facing up.
If you want neater sides, use a thin crumb coat first.
Chill the cake for 15 minutes.
Add the final layer of frosting.
Add extra chopped pecans on top if you want a finished look.
Chill the frosted cake for 20 minutes before slicing.