In a saucepan over medium heat, melt the butter. Continue cooking it for 2-3 minutes, whisking constantly, until you start to see small brown bits on the bottom of the pan.
Immediately remove the pan from the heat and pour the browned butter into a medium bowl, making sure to transfer all the browned bits as well. Let cool slightly.
Add the sugar, brown sugar and vanilla to the browned butter and stir until well combined.
Stir in the mashed banana and set aside.
In a large bowl, stir together the flour, salt, baking powder, baking soda, nutmeg and cinnamon.
Add the banana mixture and stir until well combined.
Stir in the chocolate chips. The batter will be very soft.
Refrigerate the batter for one hour.
Preheat the oven to 350°F. Line a cookie sheet with parchment paper or a silicone liner.
Roll the cookie dough into 1 1/2 tablespoon sized balls and place them 2 inches apart on the baking sheet.
Flatten the balls a bit with the palm or your hand as they won’t spread much in the oven.
Bake the cookies for 8-10 minutes, or until just set. They will still look a bit underdone, but don’t over bake them or they will dry out.
Let the cookies cool on the baking sheet for 5-10 minutes before removing them to a wire rack to cool completely. Store in a sealed container at room temperature for up to 5 days.