Preheat oven to 350°F (175°C). Grease and flour three 9-inch round cake pans.

Select very ripe bananas (black-spotted or fully brown) and mash them thoroughly in a bowl.

Drain crushed pineapple through a fine sieve, pressing gently to remove all liquid; discard the juice. Set drained pineapple aside.

Toast pecans in a dry skillet over medium heat for 3 to 4 minutes, stirring occasionally. Let cool completely before using.

In a large bowl, whisk together flour, baking soda, cinnamon, and salt. Set aside.

In a separate bowl, whisk together eggs, vegetable oil, and sugar until smooth and well combined.

Stir the mashed bananas, drained pineapple, and vanilla extract into the egg mixture until just combined.

Fold the wet ingredients into the dry ingredients using a spatula, folding just until no flour streaks remain. Do not overmix — overmixing activates gluten and makes the cake dense. The batter will be thick and lumpy from the fruit.

Fold in the cooled toasted pecans gently until evenly distributed.

Divide the batter evenly among the three prepared cake pans, smoothing the tops.

Bake at 350°F (175°C) for 25 to 30 minutes. Start checking at 25 minutes: the cake is done when the top is golden brown, the edges pull slightly from the pan sides, and a toothpick inserted in the center comes out with just a few moist crumbs (not wet batter, but not completely dry).

Remove from oven and cool in the pans for 10 minutes.

Turn the cake layers out onto wire racks and cool completely at room temperature before frosting (at least 1 hour). If in a hurry, refrigerate the layers for 30 minutes after they reach room temperature.

Make the frosting: Beat room-temperature cream cheese and softened butter together until completely smooth with no lumps, about 2-3 minutes.

Add powdered sugar one cup at a time, beating on low speed until incorporated. After all sugar is added, increase speed to medium and beat for 1 minute until light and fluffy.

Beat in vanilla extract.

Test frosting consistency: it should be spreadable but hold its shape. If too soft, refrigerate for 15 minutes before using.

Place the first cake layer on a serving plate or cake board. Spread frosting evenly over the top, extending to the edges.

Add the second cake layer and repeat: spread frosting over the top and out to the edges.

Add the third cake layer and frost the top and all sides of the cake.

Press whole or chopped toasted pecans onto the top and sides of the frosted cake for decoration.

Refrigerate the assembled cake until ready to serve. Bring to room temperature 30 to 45 minutes before serving for best frosting texture.