Step 1Heat the oven to 350 degrees. Into a large bowl sift together the flour, sugar, baking powder, baking soda and salt.
Step 2In the bowl of a stand mixer, or in a large bowl with a hand mixer, mash the bananas. Mix in the eggs, one at a time, until each is completely incorporated, then mix in the buttermilk, oil and vanilla. Finally, mix the dry ingredients into the batter just until thoroughly combined.
Step 3Pour into a 9-by-13-inch greased pan. Bake for 35 to 40 minutes, until golden-brown on top, a toothpick inserted comes out clean and the cake springs back when lightly touched. Cool on a rack.
Step 1In the bowl of a stand mixer, or in a medium bowl with a hand mixer, beat the cream cheese until smooth and there are no lumps. Add the butter and whip until incorporated, then add the powdered sugar and the sour cream. Frost the top of the cooled cake, then slice and serve.