Preheat: Preheat oven to 350 degrees Fahrenheit. Butter an 8 or 9-inch loaf pan.
Brown the butter: Place the butter (sliced into pieces) in a skillet over medium heat. Heat for a few minutes until it melts, turns foamy, and then starts to become golden brown in color and smells nutty. Immediately remove from the heat and transfer to a bowl to cool for a minute before adding to the batter.
Make the batter: Mash the bananas in the bottom of a large bowl, enough for 1 1/4 cup. Whisk in the sugar, egg, and vanilla extract. Add the browned butter once it’s ready.
Add the baking soda, cinnamon, kosher salt, all-purpose flour, and whole wheat flour to another bowl and mix. Add to the bowl with the wet ingredients and stir together with a spoon. Gently fold in 1/2 cup chocolate chips.
Bake: Pour the batter into the loaf pan and top with the remaining 1/4 cup chocolate chips. Bake 55 to 60 minutes until a toothpick inserted into the center of the loaf comes out clean (or the internal temperature is 200 degrees): the exact timing will depend on the size of the pan. Optional: add a sprinkle of flaky sea salt when you remove the bread from the oven.
Cool: Cool in the pan for 15 minutes. Then run a knife around the edge and invert the loaf onto a cooling rack. Serve warm or at room temperature. Storage info: The bread lasts 4 to 5 days at room temperature wrapped in aluminum foil, refrigerated for 10 days, or frozen for 3 months (slice it into pieces and wrap it in plastic wrap then a freezer-safe bag or container).