Preheat oven to 350 degrees. Grease and flour a 9 x 2 inch round cake pan.
Mix with electric mixer mashed bananas, granulated sugar, and brown sugar on low speed with a paddle attachment. On low speed, add the oil, eggs, sour cream, and vanilla. Mix until smooth.
In another bowl, sift together the flour, baking soda, and salt. With the mixer on low, add the dry ingredients and mix just until combined. Stir in the chopped walnuts. Pour the batter into the prepared pan and bake for 45 to 50 minutes, until a toothpick inserted in the center comes out clean. Cool in the pan for 15 minutes, then turn out onto a cooling rack, and cool completely.
Spread the frosting thickly on the top of the cake and decorate with walnut halves.
Mix the cream cheese, butter, and vanilla with electric mixer on low speed. Add the sugar and mix until smooth. Spread frosting on top of the cake.
Recipe by The Gingham Apron at https://www.theginghamapron.com/old-fashioned-banana-cake/