Start by placing the 14 tablespoons of unsalted butter in a saucepan over medium heat. Stir it frequently until it melts and begins to bubble. Keep an eye on it as it cooks; you want to achieve a golden-brown color and a nutty aroma. Remove it from heat and let it cool slightly.
In a large mixing bowl, whisk together the 2 cups of flour, 1 teaspoon of baking powder, ½ teaspoon of baking soda, 1 teaspoon of fine sea salt, ½ teaspoon of ground nutmeg, and ½ teaspoon of cinnamon. Set this mixture aside.
In another bowl, combine the brown butter (make sure it’s slightly cooled), 1 cup of granulated sugar, and ½ cup of brown sugar. Stir until well combined. Add in the 3 eggs, 2 teaspoons of vanilla extract, and 2 cups of mashed bananas. Mix until everything is well blended.
Gradually add the dry ingredients to the wet mixture, folding gently with a rubber spatula until just combined. Be careful not to overmix; it’s okay if there are a few lumps.
Preheat your oven to 350°F (175°C). Grease your loaf pan with the 2 tablespoons of room temperature unsalted butter. Pour the batter into the prepared pan, smoothing the top with the spatula. Bake in the preheated oven for 60-70 minutes or until a toothpick inserted into the center comes out clean.
Once baked, remove the banana bread from the oven and let it cool in the pan for about 10 minutes. Then, transfer it to a cooling rack to cool completely. Slice and serve plain, or with a smear of butter or your favorite spread.