How to Brown Butter: Put the butter in small saucepan and place over low heat. The butter will quickly begin to bubble and foam, swirl the pan continuously and use a whisk to stir the butter continuously. Once the butter becomes fragrant and you notice brown bits forming at the bottom, remove from the heat immediately and transfer to a small bowl. Allow to cool until lukewarm or room temperature.
Prepare Banana Bread: Preheat the oven to 350°F (175°C) with a rack in the center position. Lightly grease a 9 x 5-inch loaf pan and set aside.
In the bowl of a stand mixer fitted with a whisk attachment, mix the cooled brown butter, granulated sugar, and mashed banana until mostly smooth. With the mixer on medium speed, add the eggs one at a time beating until incorporated.
In a separate mixing bowl, whisk together the whole wheat flour, all purpose flour, almond flour, baking soda, cinnamon, salt, and nutmeg. With the mixer on low speed, add the dry flour in three additions, alternating with two additions of hot water, allowing the dry ingredients to be absorbed fully with each addition. Remove the bowl from the stand mixer and scrape down the sides and bottom of the bowl to ensure that all of the ingredients have incorporated evenly.
Transfer the batter into the greased loaf pan. Use a spatula to smooth the surface. Bake for 55 to 60 minutes or until a toothpick inserted in the center comes out clean. Set pan on a wire rack and allow the loaf to cool in the pan for 5 to 10 minutes before removing from the pan. Allow to cool completely on a wire rack before serving.