Pre heat the oven to 350˚ with the rack in the middle.
Grease a 10" cast iron skillet (or any heatproof skillet) with butter or vegetable oil.
Make the brown butter. In a small skillet, heat the butter over medium high heat until it starts bubbling. Swirl the pan and continue to cook and swirl. After a few minutes the butter will begin to foam. Reduce the heat to medium. This will subside and you will start te see brown flecks and you will smell a nutty aroma. Cook about one more minute, more flecks will appear. Continue to swirl the pan so the butter doesn't burn too quickly. Transfer the butter to a heat proof bowl. Let cool to room temperature.
Mix the cooled butter with the brown sugar in a large bowl. Mix in the egg, mashed banana and vanilla.
Whisk the flour, baking soda, salt and cinnamon together in another bowl.
Add the flour mixture into the banana mixture in two additions, combining well. Do not over mix. Fold in one-half of the chocolate chips.
Transfer the batter into the prepared skillet, smooth with top with the back of a spoon or spatula. Top with the remainder of the chocolate chips.
Bake for about 30 minutes or until a wooden skewer comes out virtually crumb free.
Remove the banana bread from the oven and let cool at least 30 minutes before slicing and serving.