Preheat oven to 350 degrees. Prepare a 9x5x3 inch loaf pan by buttering and flouring it. Use a layer of parchment paper if you prefer.
Add the flour, baking soda and salt to a large bowl, mixing until fully combined.
Brown the butter by melting butter in a saucepan over medium heat. Cook butter, scraping the bottom and sides of the saucepan with a rubber spatula until butter is golden brown and smells nutty. Watch the entire time, as butter can burn very quickly. Transfer melted butter to a separate bowl and leave it to cool to near room temperature.
When cooled, add in the mashed bananas, sugar, yogurt, eggs and vanilla extract. Stir wet ingredients until fully combined, and then add in the flour mixture. Stir dry ingredients in until just combined, and make sure not to overmix.
Pour half the banana bread batter into prepared loaf pan and spread evenly with a knife. Spoon half the Nutella over the top in dollops, and use a toothpick or skewer to swirl it into the batter. Then spoon the remaining batter over the top and spread evenly. Dollop the remaining Nutella on, then swirl it into the batter. Bake the Nutella banana bread for 55 to 60 minutes or until golden brown. Your bread is done when a toothpick inserted into the center comes out clean. Enjoy!