Preheat the oven to 350F.
Brush the inside of two 9"x5" (or 8½"x4½") pans with butter. Optionally, line with baking paper (to make lifting the baked cake out of the pan easier).
In a large mixing bowl, mash the bananas until pasty.
Pour the melted butter over the mashed bananas and stir until incorporated.
Mix in the salt, baking soda, eggs, sugar and vanilla extract.
Mix in the flour.
Pour in the buttermilk and stir just until you get a uniform consistency
Finally, stir in the nuts.
Pour the banana cake batter into the two prepared pans.
Bake the banana cake at 350F for 30 to 35 minutes.
Remove the cake pans from the oven, cool for five minutes and remove the cakes from the pans. Rest the banana cakes on a rack.
Cut the banana cakes into slices and serve. They're best while still warm.