Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 9x5 inch loaf pan.
In a medium bowl, mix together the flour, baking soda and salt. Set aside.
In a large bowl, cream together the butter and brown sugar until smooth. Beat in eggs one at a time, then stir in the vanilla. Beat in the mashed bananas.
Mix in the dry ingredients until just blended. Fold in the walnuts. Pour batter into prepared pan.
Bake for 45 to 50 minutes in the preheated oven, or until a toothpick inserted into the center of the loaf comes out clean.
Interesting Facts
Bananas are naturally high in sugar, so you can reduce the brown sugar in this recipe and still have a sweet, moist loaf of bread.
This bread can be stored in the refrigerator for up to a week.
If you don't have walnuts, you can substitute with your favorite type of nut.