Preheat the oven to 350°F (175°C) and line a muffin tin with paper liners.

In a large bowl, mix together the flour, baking soda, baking powder, cinnamon, and salt.

In another bowl, cream together the softened butter and brown sugar until light and fluffy.

Add the mashed bananas, eggs, buttermilk, and vanilla extract to the butter mixture, and mix until well combined.

Gradually add the dry ingredients to the wet ingredients, stirring until just combined.

Fold in ½ cup of the chopped walnuts.

Divide the batter evenly among the muffin cups, filling each about two-thirds full.

Sprinkle the remaining walnuts on top of the batter in each muffin cup.

Bake in the preheated oven for 20 minutes, or until a toothpick inserted into the center comes out clean.

Allow to cool in the pan for a few minutes before transferring to a wire rack to cool completely.