Steps

1. Preheat oven to 375°F. Adjust rack to center of oven.
2. Using the paddle attachment on an electric mixer, beat together the butter, sugar and salt for two minutes on medium speed. Halfway through, scrape down sides of bowl and the paddle. Add the eggs one at a time, beating on medium speed for 30 seconds after each addition. Scrape down the bowl and paddle again and beat one minute more on medium speed.
3. In a large bowl, sift together the flour, baking powder, and baking soda. In another bowl, beat together the bananas, buttermilk and vanilla.
4. With the mixer on low, add one third of the dry ingredients to the butter and eggs and beat for 30 seconds. Add half of the banana mixture and beat another minute. Continue to alternate additions of the dry ingredients and banana mixture, beating for 30 seconds after each addition. Scrape down the bowl and paddle periodically. Remove the bowl from the mixer and stir in the walnuts by hand.
5. Butter and flour a 9x4-inch loaf pan. The bottom can also be lined with buttered parchment paper if you like. Fill the loaf pan two-thirds to three-quarters full with the batter–any leftover batter can be baked in a muffin tin. Knock the pan on the tabletop two or three times to settle the batter, and place on a baking sheet.
6. Place the sheet in the oven, reduce heat to 350°F and bake 50-60 minutes, until the top is springy and a toothpick inserted in the center comes out clean. If the bread browns too quickly, drape a piece of aluminum foil over the top of the loaf pan and reduce the temperature to 325°F.
7. Cool the bread in the pan for 15 minutes, then remove and cool completely on a wire rack. Garnish by tapping powdered sugar through a sieve, slice and serve.

Notes

This is a perfect way to use up extra-ripe bananas.