Step 1Heat the oven to 350 degrees. Grease the bottoms only of 2 (8x4-inch) loaf pans or 1 (9x5-inch) loaf pan.
Step 2Mix the sugar and butter in a large bowl. Stir in the eggs. Add the bananas, buttermilk and vanilla and stir until smooth. Stir in the flour, baking powder, salt and baking soda just until the flour is moistened. Stir in the nuts. Pour the batter into the pans and smooth the tops.
Step 3Bake the loaves until a toothpick inserted in the middle comes out clean, about 1 hour 25 minutes for the 9-inch loaf and 1 hour for the smaller loaves. Cool 5 minutes. Loosen the sides of the loaves from the pans with a knife and remove the pans. Cool the loaves completely on wire racks before slicing. Store the bread tightly wrapped in the refrigerator up to 1 week.