Preheat your oven to 350°F (175°C). Grease and flour a bundt pan or two cake pans.
In a large mixing bowl, whisk together the sifted flour, granulated sugar, light brown sugar, cinnamon, nutmeg, and salt until evenly combined.
In a separate bowl, mash the bananas until smooth. Add the crushed pineapple, vegetable oil, eggs, and vanilla extract. Mix until the batter is uniform and slightly thickened.
Pour the wet mixture into the dry ingredients. Use a rubber spatula to fold everything together gently until just combined. Stir in the chopped pecans.
Transfer the batter into the prepared pan(s), smoothing the top with a spatula. Place in the oven and bake for 50-60 minutes, until the surface is golden brown and a toothpick inserted in the center comes out clean.
Remove the cake from the oven and let it cool in the pan for 15 minutes. Then, transfer to a wire rack to cool completely before frosting or slicing.