Preheat the oven to 350 degrees F. Line a pullman or 9 inch square pan with parchment paper, leaving the ends hanging over the sides for easy removal.
In a medium bowl, combine the flour, baking powder, and salt. Set aside.
Brown the butter: In a small saucepan, add 227g (16 tbsp) of unsalted butter and place over medium heat. As the butter melts, stir it with a rubber spatula to encourage even cooking. Once the butter has fully melted, it will alternate between rapid large bubbles and gentle small foamy bubbles. The butter will be ready once it turns a dark golden color and the fat solids have darkened and settled at the bottom of the pan. Immediately pour into a large bowl, scraping out the fat solids at the bottom, and weigh out to 184g (13 tbsp).
To the brown butter, whisk in the brown sugar and granulated sugar. Then, vigorously whisk in the egg, egg yolk, and vanilla until fully combined.
On a medium plate, mash the bananas until smooth. Whisk the mashed bananas into the batter.
Add the dry ingredients to the batter and use a rubber spatula to fold until just combined.
Pour the batter into the prepared pan, then dollop the Nutella on top and use a toothpick to swirl it in.
Bake the banana blondies for about 30 minutes until evenly golden. Allow them to cool completely in the pan before removing and cutting into 16 squares.