Preheat the oven to 350°F (180°C). Grease the loaf pan with 2 teaspoons of the butter, then dust the pan with 2 teaspoons of the coconut flour, tapping out any excess.
Place the remaining 7 tablespoons plus 1 teaspoon butter in a small saucepan and melt it over medium-low heat. Let simmer, stirring occasionally, until golden brown and nutty smelling, 5 to 8 minutes. Set the browned butter aside to cool.
In a large bowl, whisk together the remaining 4 tablespoons plus 1 teaspoon coconut flour, the almond flour, ground flaxseed, baking powder, xanthan gum, cinnamon, nutmeg, and 3/4 teaspoon salt. Set aside.
In another large bowl, combine the eggs and sweetener and beat with an electric mixer on medium speed, until fluffy and lighter in color, about 2 minutes. Reduce the mixer speed to low and add the banana and vanilla extracts, apple cider vinegar, and browned butter.
Add the flour mix to egg mix in three parts, alternating with sour cream, beginning and ending with flour. Mix until a fully incorporated, thick batter, 2 to 3 minutes. Fold in half of the walnuts.
Pour the batter into the prepared loaf pan. Dip a spoon in water, then use the back of the wet spoon to smooth the batter. Sprinkle the remaining walnuts on top, then bake until the top is deep golden and a toothpick inserted into the center of the loaf comes out clean, 50 to 55 minutes. After 30 minutes of baking, check the bread; if you see deep golden-brown areas on the crust and walnuts, gently tent the loaf pan with aluminum foil for the remainder of baking. Let cool in the pan on a wire rack for 15 minutes.
Carefully remove the bread from the pan and let it cool completely on a wire rack before slicing, 50 to 60 minutes. Serve.