Brown butter in a light-coloured saucepan over medium heat. Swirl occasionally until milk solids are deep amber and butter smells nutty. Pour immediately into a large mixing bowl including all browned bits. Cool for 10 minutes.
Mash overripe bananas thoroughly with a fork until almost smooth. Measure out ¾ cup. Set aside.
Add both sugars to cooled browned butter. Whisk vigorously for 2 minutes.
Add egg, egg yolk, and vanilla extract. Whisk for 1 to 2 minutes until smooth and slightly ribbony.
Add mashed banana. Stir to combine.
Whisk flour, baking soda, baking powder, cinnamon, nutmeg, and salt together in a separate bowl.
Fold dry ingredients into wet ingredients with a rubber spatula until the last streak of flour disappears. Do not overmix.
Fold in chocolate chips evenly.
Cover bowl tightly with cling wrap. Refrigerate for minimum 30 minutes.
Preheat oven to 180°C (350°F). Line two baking sheets with baking paper.
Scoop dough into 45g balls. Place on prepared baking sheets with 5cm between each.
Press extra chocolate chips onto tops if using. Sprinkle each ball with flaky sea salt.
Bake for 10 to 12 minutes until edges are golden and set. Centres should still look slightly underdone.
Remove from oven. Bang trays on counter once or twice from a low height.
Cool on tray for 5 minutes. Transfer to wire rack.