Preheat oven to 350° F. Grease and line three 6-inch round cake pans with parchment paper. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment, cream butter until smooth. Add sugar and continue to mix until well combined. Scrape down sides of bowl as needed.
Add eggs one a time and mix until incorporated. Add vanilla and mashed bananas. Mix until combined.
In a medium bowl, whisk together flour, baking soda, baking powder, and salt. In another bowl, mix together milk and sour cream. (It does not need to be smooth)
Add 1/3 of dry mixture to mixing bowl and mix on low speed. Follow with half of milk mixture. Repeat and end with remaining 1/3 of dry mixture. Mix until there are no longer any dry streaks of flour in batter.
Distribute batter evenly among prepared cake pans. Smooth and level batter using a mini offset spatula or spoon. Bake for 30-35 minutes, rotating pan midway through baking. Insert toothpick in center of cake to check for doneness. If toothpick does not come out clean, bake for another 5-8 minutes.
Let cake cool in pan for 5 minutes. Loosen cake edges from pan using a mini offset spatula. Remove cake from pan and let cool to room temperature on wire rack.