Prepare the Batter: Preheat the oven to 180°C (350°F). In a bowl, beat together the melted butter and sugar until light and fluffy. Add the mashed bananas, eggs, and vanilla extract, mixing until well combined.
Combine Dry Ingredients: In a separate bowl, whisk together the flour, baking soda, baking powder, and salt. Slowly add the dry mixture to the wet ingredients, stirring just until combined.
Add Walnuts: Gently fold in the chopped walnuts until evenly distributed throughout the batter.
Bake the Loaf: Grease a loaf tin and pour in the batter, smoothing the top. Bake for 50-60 minutes, or until a skewer inserted in the center comes out clean. Let it cool in the tin for 10 minutes before transferring to a wire rack to cool completely.