Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake 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 using an electric mixer.
Add the eggs one at a time to the butter and sugar mixture, beating well after each addition.
Mix in the vanilla extract.
Add the mashed ripe bananas and sour cream to the wet mixture and stir until combined.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined. Do not overmix.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 40 to 45 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.
Turn the cake out onto a wire rack and let it cool completely before serving.