Preheat the oven to 350F. Grease bottom only of an 8 ½ by 4 ½ inch loaf pan. If desired, line vertically with a strip of parchment paper to make a sling.
In a large mixing bowl, mix together the self rising flour and the sugar. Add the eggs, buttermilk and vanilla and stir until well blended, then stir in the oil.
Lastly, mash the bananas and stir them into the batter along with the nuts.
Spread batter evenly in the baking pan and bake for 60-65 minutes.
Let cool in the pan for a few minutes, then carefully loosen sides by sliding a knife between the loaf and the pan.
Let cool until bread feels sturdy enough to lift from pan, then remove from pan and set on a rack to cool completely.
Notes
Adapted from The Culinary Institute of America's "Breakfast and Brunches" and Martha White.