Preheat oven to 350 degrees Fahrenheit (175 degrees Celsius) and grease a 9x9 inch baking pan.
In a large bowl, cream together 1/2 cup softened butter and granulated sugar until light and fluffy.
Beat in the egg and 1 teaspoon of vanilla extract, then fold in the mashed bananas.
In a separate bowl, whisk together flour, baking soda, salt, and cinnamon.
Gradually add the dry ingredients to the wet ingredients, stirring until just combined.
Pour the batter into the prepared baking pan and bake for 45 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool completely on a wire rack before frosting.
To make the frosting, beat together the cream cheese and 1/4 cup softened butter until smooth.
Gradually add the powdered sugar and 1 teaspoon of vanilla extract, beating until creamy.
Spread the frosting evenly over the cooled cake before serving.