Preheat your oven to 350°F (175°C) and grease a 9x13-inch baking pan.
In a large bowl, cream butter and sugar until light and fluffy. Beat in eggs, one at a time. Stir in sour cream, vanilla extract, and mashed bananas.
In another bowl, whisk together flour, baking soda, and salt. Gradually add to the creamed mixture, mixing just until combined.
Spread batter evenly into the prepared baking pan.
Bake for 25 minutes, or until a toothpick inserted into the center comes out clean. Let cool completely.
For the frosting: Beat together the softened butter and cream cheese until smooth. Gradually add powdered sugar and vanilla extract, beating until fluffy.
Spread the cream cheese frosting over the cooled banana bars. Cut into squares and serve.