Reheat the oven to 350 degrees F. Grease a 13 x 9-inch baking pan using baking spray.
Cream the butter and sugars in the bowl of a stand mixer fitted with the paddle attachment for about 4 minutes on high, scraping down the sides of the bowl with a rubber spatula as necessary.
Add the eggs one at a time, blending each time until incorporated.
In a small bowl, dissolve the baking soda, baking powder, and salt into the sour milk. Alternately add the milk mixture and flour to the creamed butter mixture, starting and ending with the flour (add the flour in 1/2-cup increments), mixing to fully incorporate the ingredients each time.
Blend in the oats and mashed bananas. With the mixer on low, beat for 30 seconds.
Pour the batter into the prepared pan and bake for 20 to 25 minutes, until the top is golden and a toothpick inserted into the center of the cake comes out clean. Remove from the oven and let the cake cool completely in the pan.
Meanwhile, make the cream cheese frosting:
In bowl of an electric mixer fitted with the paddle attachment, cream the butter and cream cheese for 2 minutes on high, scraping down the sides of the bowl with a rubber spatula as necessary. Sift the confectioners' sugar into the bowl and beat for another 2 minutes, or until smooth. Add the vanilla extract and salt and beat on high for another 30 seconds.
Reprinted with permission from Sweet Home by Rebecca Miller, Kyle Books copyright (c) 2012