Preheat oven to 350°. In a stand mixer with paddle, cream butter vanilla, and sugar until light and fluffy, 5-7 minutes. Add the bananas and turn up to medium until they are well blended and no big pieces remain. Add the baking soda and mix well. Scrape down the bowl and mix again.
Add the eggs and mix well. Then add the flour on low speed just until combined.
Scrape into a greased or parchment lined 9x13 pan.
Bake for about 20 minutes until the top is nicely dark golden and a toothpick in the center comes out clean. It goes from golden to burning quick, so check around 15 minutes and watch closely.
Allow to cool completely before frosting.
For the frosting:
Add the cream cheese to the mixer with paddle attachment and beat until very smooth and no lumps remain. Add the butter and beat again until smooth.
Add the vanilla and powdered sugar and mix well. Beat until fluffy and spread on the cooled cake.