Preheat oven to 375 degrees F. Place liners inside the wells of a muffin pan.
Put the butter in large bowl and beat until creamy. Add the sugar and blend well. Stir in the banana purée and eggs, and beat until the batter is light and smooth.
In a medium bowl, add the flour, bran, salt and baking soda to a large bowl and mix until combined. All at once, add the dry ingredients to the wet ingredients and mix until combined; being sure not to over mix. Next, gently fold in the walnuts. Spoon the batter into muffin pans, almost filling them. Bake 15 to 20 minutes. Serve warm.
!Recipe adapted from Marion Cunningham