Preheat the oven to 350 degrees F. Grease with butter and dust with flour three 9- or 10-inch round cake pans.
In a medium bowl, whisk the flours, sugar, salt, spices and baking soda.
In a big bowl, whisk the oil, eggs, egg yolks, buttermilk, vanilla, pineapple and bananas really well.
Add the flour mixture into the wet mixture and whisk gently until there are no lumps. Fold in 3/4 cup of the pecans.
Divide the batter among the pans, scraping all the batter from the bowl with a rubber spatula. Bake for 35 to 50 minutes, depending on your oven. Be advised: This is a dense, moist cake and you'll be tempted to overbake it. Try not to. Once you start seeing color on top, keep pressing the top of the cake. When it's firm, it's done.
Turn out the cake layers onto a wire rack and let them cool completely. Frost with cream cheese frosting and garnish with the remaining 3/4 cup pecans and--if you're feeling very Southern--sliced maraschino cherries. You can even brulee some pineapple slices for the top of the cake.
Cream Cheese Frosting:
In the bowl of a stand mixer fitted with the paddle attachment, combine all the ingredients. Whip on low speed for a while. When the sugar is incorporated, turn the mixer speed up and beat until smooth, scraping the sides of the bowl often.
To spread, use the frosting at room temperature, but store it covered in the fridge. Rewhip cold frosting before using it.