Preheat your oven to 350° F. Grease and flour a standard loaf pan and set aside.
In a medium frying pan on medium heat add the 1/2 cup of butter. Melt it and keep stirring until the butter starts to foam. Once the butter foams it will brown quickly after so keep stirring. As soon as it turns dark golden brown remove from heat and pour into a heat-proof bowl to cool slightly.
Once the butter has cooled to just warm, add the sugar in and stir together until smooth and combined.
Add in the eggs, one at a time, beating until smooth.
Mix in the mashed bananas, then stir in the vanilla.
In a separate bowl whisk together the dry ingredients.
Stir in gently, until just combined. If using the chocolate chips, stir in now.
Pour into the prepared loaf pan.
Bake in the oven for 50-60 minutes, until a cake tester or toothpick inserted comes out clean. If the top starts to brown too quickly, cover with foil lightly.
Remove and cool in the pan for 10 minutes, then release from the pan and cool on a baking rack.
Keep wrapped or in a container for up to 5 days at room temperature.
Notes
As with all banana bread, if the top starts to get too brown, tent the top lightly with aluminum foil and continue baking.