Preheat your oven to 350°F (175°C). Grease and flour a baking pan.
In a mixing bowl, cream together the butter and sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
In another bowl, whisk together the flour, baking soda, and salt. Gradually add to the creamed mixture, mixing just until combined.
Fold in the mashed bananas. Pour the batter into the prepared baking pan.
Bake for 30 minutes or until a toothpick inserted into the center comes out clean. Allow the cake to cool completely.
For the frosting, beat together the cream cheese and butter until smooth. Gradually add the powdered sugar and vanilla extract, beating until creamy.
Spread the frosting over the cooled cake. Slice and serve.