Preheat the oven to 350 degrees F. Line a pullman or 9x5 inch loaf pan with parchment paper, leaving the ends hanging over the sides for easy removal.
In a medium bowl, combine the flour, baking powder, baking soda, cinnamon, nutmeg, and salt. Set aside.
Brown the butter: In a small saucepan, add 155g (11 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 113g (8 tbsp). Pour the remainder into a small bowl, and place in the fridge to solidify.
To the brown butter, whisk in the brown sugar and granulated sugar. Then, vigorously whisk in the egg and vanilla until fully combined.
On a medium plate, mash the bananas, leaving them slightly chunky or smooth depending on texture preference. Whisk the mashed bananas into the batter.
Whisk in half of the dry ingredients until just combined. Mix in the yogurt, then the remaining dry ingredients until fully combined.
Pour the batter into the prepared loaf pan and smooth out the top. Add a generous sprinkling of turbinado sugar.
Transfer the remaining solidified brown butter to a piping bag and snip the end off. Use a knife to draw a straight line down the center of the batter. Pipe the brown butter along the line.
Bake the banana bread for 60-75 minutes or until deeply golden and a toothpick inserted comes out clean. Remove from the pan and allow to cool completely before cutting.