Preheat oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
In a large bowl, cream together the butter and sugar until light and fluffy. Beat in eggs one at a time, then stir in the vanilla.
In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add to the wet ingredients, alternating with the sour cream, beginning and ending with the dry ingredients. Mix until just combined.
Stir in the mashed bananas.
In a small bowl, beat together the cream cheese, powdered sugar, and vanilla until smooth. Spread half of the batter into the prepared pan. Dollop the cream cheese mixture evenly over the batter, then top with the remaining batter.
Bake for 35-40 minutes, or until a wooden skewer inserted into the center comes out clean.
Let cool completely before serving.
Notes
Store leftover cake in an airtight container at room temperature for up to 3 days or in the refrigerator for up to a week.