If you plan on baking off the muffins right away, preheat the oven to 425°F / 220°C and alternate lining a muffin pan with 6 parchment liners. If you plan on letting the batter rest, proceed with this step after letting the batter rest.
Add the butter to a small saucepan set over medium heat. Stir the butter occasionally until it turns amber in color and develops little brown specks. Take the butter off the heat and transfer to a small bowl. Set the butter in the freezer for 5 minutes to cool off.
In a medium-sized mixing bowl, mash the banana to your desired consistency.
To the banana, add in the cooled brown butter, sugar, egg, sour cream, and vanilla. Whisk until well combined.
Add in the flour, baking powder, baking soda, and salt. Lightly fold the mixture together until only a few flour streaks remain. Then, add in the chocolate chips and fold the mixture just until the last streak of flour dissapears.
(OPTIONAL) Cover the bowl with plastic wrap and let the batter rest at room temperature for at least 30 minutes and up to 1 hour before baking. This will encourage a more flavorful, higher-rising muffin!
Evenly distribute the muffin batter between the six parchment liners, filling each liner to the very top.
Add the nutella to a piping bag fitted with a large round tip, and pipe ~1 tbsp. of nutella into the center of each muffin.
(OPTIONAL) In a small bowl, melt some nutella. Drizzle a little bit of nutella over each muffin, then use a toothpick to swirl it around on top.
Bake the muffins at 425°F for 5 minutes. Without opening the oven door, reduce the temperature to 350°F / 175°C. Bake for an additional 10-15 minutes, or until a toothpick inserted into the center of the muffins comes out clean.
Serve and enjoy!