Preheat the oven to 350°F (175°C). Grease and flour an 8×8 inch baking pan.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition.
Stir in the vanilla extract and mashed bananas until well combined.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the banana mixture, alternating with the sour cream, beginning and ending with the dry ingredients. Mix until just combined.
Pour the batter into the prepared baking pan and smooth the top with a spatula.
Bake in the preheated oven for 35 minutes or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes.
Transfer the cake to a wire rack to cool completely before slicing into 8 equal pieces.
Serve each slice on a dessert plate. Optionally, garnish with a light dusting of powdered sugar or a small dollop of whipped cream.