In a small bowl, mix the vinegar and milk. Set aside.
Using an electric mixer (or a stand mixer with a paddle attachment), cream together the butter and sugar until it's fluffy (2 - 3 minutes). Add the eggs, milk, and vanilla, and mix until well combined. Stir in the mashed banana.
Add the flour, baking powder, baking soda, and salt and mix until well combined. The batter will be on the thick side.
Spread the batter evenly into a greased 9x13" baking pan and bake in a 350℉ oven for 25 to 30 minutes, until a toothpick inserted in the center of the cake comes out clean. Allow to cool completely.
While the cake is cooling, prepare the cream cheese frosting. Using an electric mixer (or stand mixer with the whisk attachment), beat together the butter, cream cheese, and vanilla.
Add the powdered sugar about half a cup at a time, and beat until smooth. Spread the frosting evenly over the top after cake has completely cooled. Top with fresh sliced bananas immediately before serving.
Notes
Calories are automatically generated. For best results calculate based on your exact ingredients.