Preheat oven to 350 degrees F and line a cake pan with parchment paper.
Add in the eggs, one at time, whisking until just incorporated.
In a large bowl, whisk together the butter and sugars until smooth.
Add in the vanilla and the mashed bananas, mixing well.
Mix in half of the flour, baking powder, baking soda and salt.
Slowly add in remaining flour and all of the milk and mix until incorporated.
Pour cake batter into the prepared pan and bake for 40 minutes, or until a toothpick inserted in the center comes out clean. Remove from oven and let cool while you prepare the frosting. Cake can be served directly from the pan.
Make the frosting: In a large bowl, mix the room temperature cream cheese and butter together until smooth.
Add in the vanilla and pinch of salt. Stir to combine.
Slowly add in the confectioner's sugar and stir until smooth and spreadable.
Frost the cooled cake and serve. Store any leftovers in the refrigerator.