Start by browning the butter. Add the butter to a small pan and put it over medium heat stirring occasionally. Remove from the heat once you see brown specks beginning to form at the bottom of the pan. Pour it into a medium mixing bowl.
Add the brown sugar and mix until well combined. Then add the egg yolk and vanilla extract and incorporate. Fold in the flour, baking powder, and salt.
In a separate bowl, mash the banana until there are no big chunks. Add it to the batter along with the chocolate chips (or chocolate chunks) and mix until just combined.
Cover your batter tightly and put it in the fridge for at least 1 hour, or overnight if possible.
Preheat the oven to 425 °F and line the cupcake tins. Fill the muffin pan almost all the way to the top.
Bake for 10-12 minutes at 425 °F. The muffins should be about ¼” to ½” above the paper. Reduce the temperature to 350 °F and bake for 10-12 minutes or until a toothpick inserted comes back clean. Do not open the door when reducing the temperature.