To make the cake, Preheat the oven to 350 degrees F. Butter and flour two 8-inch round cake pans and line with parchment paper.
Spread the pecans on a baking sheet and bake until fragrant and toasted, about 5 minutes. Let cool slightly, then roughly chop. Toss with the smashed bananas, chopped pineapple and 1/2 cup flour in a small bowl.
Whisk the remaining 2 1/4 cups flour, spices, baking soda and salt in a medium bowl and set aside.
Beat the eggs and granulated sugar in a separate bowl with a mixer on high speed until thick and light, about 5 minutes. Gradually beat in the oil, streaming slowly on the side.
Sprinkle the flour mixture over the egg mixture in two parts, gently folding to make a thick batter. Fold in the pecan-fruit mixture.
Transfer the batter to the prepared pans. Bake until the cakes are firm and a toothpick inserted into the middle comes out clean, 45 to 50 minutes. Cool in the pans on a rack, 25 minutes, then invert the cakes onto the rack to cool completely.
To make the frosting, Beat the cream cheese in a large bowl with a mixer until fluffy, then gradually beat in the butter until combined. Sift the confectioners' sugar over the cream cheese mixture and beat until smooth. Add the lemon zest and vanillas and beat until light and fluffy. Add pecans pieces and mix well.
Place one cake layer on a serving plate. Spread about half of the frosting on top, then cover with the other cake layer. Spread the remaining frosting over the top and sides of the cake. Store in fridge until ready to eat.