Preheat oven to 350°F (175°C). Grease and line two 9-inch cake pans.
Mash ripe bananas until smooth with a few small lumps remaining.
In a bowl, whisk together flour, baking soda, baking powder, salt, and cinnamon.
Cream butter, granulated sugar, and brown sugar until pale and fluffy.
Add eggs one at a time, then mix in vanilla extract.
Stir in mashed bananas and sour cream until combined.
Fold dry ingredients into wet ingredients until just combined.
Divide batter between prepared pans.
Bake for 30–35 minutes or until a toothpick inserted in the center comes out clean.
Cool cakes in pans for 10 minutes, then transfer to a wire rack to cool completely.
Beat cream cheese and butter until smooth. Add powdered sugar, vanilla, and salt and mix until creamy.
Frost the cooled cake and serve.