Preheat oven to 350F. Grease and line the bottom and sides of a 9-inch square cake pan with parchment paper.
In a medium-sized bowl, whisk together the flour, baking soda and salt.
In a separate large bowl, whisk together the granulated sugar, brown sugar and oil.
Whisk in the mashed banana, sour cream, egg and vanilla.
Add the flour mixture to the wet ingredients and stir until just combined. Be careful not to over mix.
Pour the batter into the prepared cake pan. Bake for 21-23 minutes, or until browned and a tooth pick inserted into the middle comes out clean.
Let fully cool in the pan before frosting.
For the frosting, use an electric mixer to cream together the butter and sour cream. Add the powdered sugar and vanilla and beat until smooth and creamy. (Add the milk for a thinner frosting or more powdered sugar for a sweeter and thicker frosting).
Spread the frosting onto the cooled cake. Slice and serve immediately, or store covered in the fridge to enjoy later.
Notes
Full fat sour cream will range from 14% to 18% milk fat. I prefer 18% for this recipe, especially for the frosting as thicker sour cream will create a thick and creamy frosting.
I used vanilla bean paste in the frosting for maximum vanilla flavor but vanilla extract works great too.
You can turn this recipe into banana bread by baking it in a 9x5 inch loaf pan. Just reduce the oven temperature to 325F and bake for 45-50 minutes.