Preheat oven to 375. Prepare cupcake pans with liners.
Make The Brown Butter
Place the butter in a saucepan over medium heat. Stirring occasionally, keep the butter on the stovetop while it hisses and pops.
After a few minutes, the mixture will start to rapidly bubble up. Shortly after, you'll start to see some brown bubbles in the sea of yellow. This is when you know you're done!
Remove from the heat and stir. Allow to cool to room temperature (this can be sped up by putting the brown butter in an ice bath).
Make the Batter
Combine butter, eggs, and vanilla in a bowl. Mash bananas and add to mixture.
In a separate bowl, combine flour, brown sugar, baking soda, baking powder, salt, and cinnamon.
Slowly add flour mixture into banana mixture. Mix until fully combined. Add in walnuts if desired.
Bake!
Spoon about ¼ cup of the batter into the cupcake liners, then sprinkle the top of the muffins with coarse sugar if desired.
Bake for 13-15 minutes or until a toothpick comes out clean.
Notes
Store in an airtight container for up to 3 days, or freeze for up to 3 months.