Preheat oven to 350°F (177ºC) and prepare parchment-lined loaf pan.
In a large mixing bowl, whisk together eggs, butter, dark brown sugar and vanilla. Add mashed banana to egg mixture and continue whisking until the banana starts to break down.
Stir in flour, baking soda, cinnamon and salt plus half (¼ cup) of the chopped walnuts just until combined (still lumpy!).
Pour banana bread batter into loaf pan and sprinkle the remaining walnuts across the top of the loaf. Bake for 50-55 minutes until golden and a tester comes out dry. Transfer to a wiring cooling rack and let sit until the top cools (about 30 minutes). To remove from pan, lift using parchment edges and place on cutting surface. Slice with a sharp knife and serve warm with lots of melty butter!