Preheat oven to 350°. Coat a 9x5x3" loaf pan with nonstick spray. Whisk flour, baking soda, and salt in a medium bowl. Whisk eggs, sugar, bananas, walnuts and oil in a large bowl until smooth. Add dry ingredients to banana mixture and walnuts stir just until combined. Scrape batter into prepared pan and smooth top.
Bake until a tester inserted into the center of bread comes out clean, 60-70 minutes. Transfer to a wire rack; let bread cool in pan for 15 minutes. Run a knife around inside of pan to release the bread. Turn out onto rack and let cool completely.