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, about 3-4 minutes.
Add the eggs one at a time to the butter and sugar mixture, beating well after each addition.
Stir in the mashed ripe bananas, sour cream, and vanilla extract until combined.
Gradually add the dry ingredients to the wet ingredients, mixing gently until just combined. Do not overmix.
Pour the batter into the prepared baking pan and spread evenly.
Bake in the preheated oven for 35-40 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 and serving.