Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 9x13-inch pan.

Make cake: In a large bowl, beat sugar, butter, eggs, and vanilla until creamy.

In another bowl, sift together flour, baking powder, baking soda, and salt. Add dry ingredients to the wet ingredients. Add mashed bananas and sour milk and mix until combined. Pour into the prepared pan.

Bake in the preheated oven for 25 to 40 minutes. Remove from the oven and let cool to room temperature.

Meanwhile, make frosting. Mix frosting and mashed banana together until well combined. Spread over cooled cake. Sprinkle with confectioners' sugar.