Preheat the oven to 350°F (176°C). Prepare three 8-inch cake pans with parchment paper and grease the sides.

In a medium bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Set aside.

In a large mixer bowl, beat together butter, oil, brown sugar, white sugar, and vanilla until light and fluffy, about 2-3 minutes.

Add eggs one at a time, mixing well after each, then add egg white. Scrape down the sides of the bowl.

Gradually add dry ingredients to the wet mixture and mix until just combined.

Fold in mashed bananas, crushed pineapple, and chopped pecans gently.

Divide the batter evenly into the prepared pans and bake for 27-30 minutes, or until a toothpick inserted in the center comes out clean.

Cool the cakes in the pans for 5 minutes, then transfer to wire racks to cool completely.

For the frosting, beat together cream cheese and butter until smooth. Gradually add powdered sugar and vanilla, beating until creamy.

Assemble the cake: Level the cakes if necessary, spread frosting between layers, and frost the outside of the cake. Decorate as desired.