Preheat oven to 350 degrees F. Grease or line with parchment paper a 9×5 bread pan.
Make your brown butter by adding the butter to light colored pan over medium heat. Place a medium saucepan over medium-low heat. Add stick of butter. Melt the butter, making sure to stir occasionally. Do not walk away from the stove as the process can go quickly once the butter melts. The butter will start to bubble and sizzle a little bit.
After about 5-8 minutes, the milk solids in the butter will start to brown. Stir continuously until you have reached a golden-brown color. Remove from heat immediately to prevent the butter from burning. I like to transfer my browned butter to a separate bowl and place in the refrigerator to let it cool slightly before adding it the batter. You do not want to add hot butter to the batter.
To make the banana bread, combine the flour, salt and baking soda in a medium bowl. Whisk together and set aside.
In a separate large mixing bowl, add the eggs, brown sugar and granulated sugar. Whisk together or use a electric hand mixer until fully combined. Add the bananas and mash down. Pour in the cooled brown butter, Greek yogurt and vanilla extract. Mix together until fully combined.
Add the flour mixture to the wet ingredients and stir until just combined. Be careful not to overmix the batter. Pour or scoop the batter into the loaf pan. Bake for 55-60 minutes or until the batter is fully set. The banana bread is done when a toothpick comes out clean.
The nutrition facts provided are calculated using a third-party tool and are estimates only. Actual nutritional content may vary based on the ingredients and brands you use, as well as portion sizes. For accurate results, please consult a registered dietitian or nutritionist.