Preheat the oven to 350°F / 175°C. Butter and line a 9x5" loaf pan with parchment paper.
In a small saucepan set over medium heat, brown the butter. Stir the butter occasionally until it turns amber in color and develops little brown specks. Take the butter off the heat and let cool in the fridge for 10 minutes or until it is not hot, but still melted.
Microwave the cookie butter for 30 seconds, or until it has a more liquid consistency.
In a medium sized mixing bowl, mash the banana.
Whisk in the brown butter, granulated sugar, and 100g (⅓ c. + 1 tbsp.) of the melted cookie butter.
Whisk in both eggs, the vanilla, and sour cream until very well combined.
Add in the flour, baking powder, baking soda, and salt. Fold the mixture together with a rubber spatula until almost all of the flour has been incorporated. Add in the walnuts and fold just until no flour streaks remain.
Pour half of the banana bread batter into the prepared loaf pan. Drizzle half of the remaining cookie butter over the batter, then use a knife to swirl it around.
Pour the remaining banana bread batter into the pan, and swirl the remaining cookie butter on top of it.
Bake the bread for 50-60 minutes or until a toothpick inserted in the middle of the bread comes out clean. Let the bread cool to room temperature before slicing.
Serve and enjoy!