Preheat the oven to 350°F (175°C). Grease and flour an 8-inch square baking pan.
In a medium bowl, whisk together the all-purpose flour, baking soda, and salt. Set aside.
In a large bowl, cream the softened unsalted butter and granulated sugar together until light and fluffy.
Beat in the eggs one at a time, then stir in the vanilla extract.
Mix in the mashed ripe bananas and sour cream until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing just until incorporated.
Fold in the chopped walnuts gently.
Pour the batter into the prepared baking pan and spread evenly.
Bake in the preheated oven for 35 to 40 minutes, or until a toothpick inserted into the center comes out clean.
Remove from oven and allow the cake to cool in the pan for 10 minutes.
Turn the cake out onto a wire rack and cool completely before slicing into 8 equal pieces.
Serve each banana cake slice plain or with a dusting of powdered sugar or a dollop of whipped cream if desired.