Preheat oven to 350° F. Line two 6-inch cake pans with parchment and lightly grease the sides.
Whisk together flour, baking soda, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment, cream butter. Add sugar and brown sugar and mix until well combined. Add eggs one at a time. Add mashed bananas. Scrape down bowl as needed to ensure thorough mixing.
Alternate adding flour mixture and milk. Start with the flour and end with the flour. Mix until just combined.
Divide batter evenly between the two prepared cake pans. Bake for 30-35 minutes until toothpick inserted in center of cake comes out clean. Let cool in pan for a few minutes before unmolding. Transfer to wire rack to cool to room temperature.