Preheat your oven to 350°F (175°C). Grease and flour a 9-inch cake pan. In a bowl, whisk together flour, baking soda, and salt.
In another bowl, beat butter, granulated sugar, and brown sugar until light and fluffy. Add eggs one at a time, followed by vanilla extract. Stir in the sour cream and mashed bananas.
Gradually mix the dry ingredients into the wet mixture until just combined. Pour the batter into the prepared pan and smooth the top. Bake for 30-35 minutes or until a toothpick inserted in the center comes out clean.
Allow the cake to cool in the pan for 10 minutes, then transfer to a wire rack. Serve plain, with powdered sugar, or topped with cream cheese frosting.