1. Preheat the oven to 350°F (175°C). Grease a 9 x 5-inch (23 x 13 cm) loaf pan and line it with parchment paper, leaving an overhang on the long sides.

2. Brown the butter: melt all of the butter (1/2 cup plus 2 tablespoons) in a light-colored saucepan over medium heat, stirring often. It will foam, then turn golden with brown flecks and smell nutty, about 5 to 7 minutes. Measure out 2 tablespoons of the brown butter into a small bowl for the glaze. Pour the rest into a large heatproof bowl, scraping in all the brown bits, and let it cool for 10 minutes.

3. Mash the bananas in a separate bowl until mostly smooth with a few small lumps.

4. Whisk the brown sugar into the cooled brown butter. Whisk in the eggs one at a time, then the vanilla.

5. Stir in the mashed bananas.

6. Sprinkle the baking soda, salt, and cinnamon over the batter, then add the flour. Fold with a spatula until just combined, with a few streaks of flour remaining. Fold in the 1/2 cup of pecans. Do not overmix.

7. Pour the batter into the prepared pan and smooth the top.

8. Bake for 55 to 65 minutes, until the top is deep golden and a toothpick inserted in the center comes out clean or with a few moist crumbs. If the top browns too quickly, tent it loosely with foil.

9. Cool in the pan for 15 minutes, then lift out using the parchment and cool completely on a wire rack.

10. Whisk the reserved brown butter, powdered sugar, maple syrup, and enough milk to make a thick, pourable glaze. Spread over the cooled loaf, sprinkle with the remaining 2 tablespoons of chopped pecans, let set for 15 minutes, and slice into 10 slices.