Sift together the flour, sugar, baking soda, baking powder, and salt.
In your mixer mash the bananas.
Mix in the eggs one at a time until each is completely incorporated.
Then mix in the buttermilk, oil and vanilla.
Then mix the dry ingredients into the batter just until thoroughly combined.
Pour into a 9X13 inch greased pan and bake for 35-40 minutes until golden brown and toothpick comes out clean.
Cool on a rack.
I doubled this recipe and used three fourths whole wheat pastry flour and the other one fourth white pastry flour. I also sifted the flours but I don't know if its needed?Came out great. Very fluffy, moist and sweet. I didn't frost it.