Preheat your oven to 350°F (175°C). Grease a 9x5-inch loaf pan with butter or non-stick cooking spray.
In a medium bowl, whisk together the all-purpose flour, baking soda, and salt until well combined. Set this dry ingredient mixture aside.
In a large mixing bowl, use an electric mixer on medium speed to cream together the softened butter and brown sugar until the mixture is light, fluffy, and pale in color, about 2-3 minutes. Beat in the eggs one at a time, followed by the mashed bananas and vanilla extract, until just combined.
Gradually add the dry flour mixture to the wet ingredients, mixing on low speed or by hand with a spatula until the flour is just incorporated. Be careful not to overmix. If using, gently fold in the chopped walnuts.
Pour the batter into the prepared loaf pan and spread it evenly into the corners. Bake for 60 to 65 minutes, or until a toothpick or cake tester inserted into the center of the loaf comes out clean.
Let the banana bread cool in the pan on a wire rack for 10 minutes. Then, carefully remove the loaf from the pan and allow it to cool completely on the wire rack before slicing.