Brown the butter: Place 6 tablespoons (85 grams) of unsalted butter in a medium saucepan over medium heat. Stir occasionally as it melts, then watch carefully as it starts to foam and the milk solids turn golden brown (about 5-7 minutes). Smell for a rich, nutty aroma. Immediately remove from heat and pour into a heatproof bowl to cool slightly.

Toast the walnuts: While the butter browns, heat a dry skillet over medium heat. Add ¾ cup (90 grams) chopped walnuts and toast for 3-4 minutes, stirring frequently until fragrant and lightly browned. Transfer to a plate to cool.

Preheat oven to 350°F (175°C). Line a 9×5-inch loaf pan with parchment paper, leaving some overhang for easy removal.

Mix wet ingredients: In a large bowl, combine mashed bananas, browned butter, granulated sugar, brown sugar, eggs, and vanilla extract. Whisk gently until smooth but do not overmix; a few lumps are fine.

Combine dry ingredients: In a separate bowl, whisk together flour, baking soda, and salt.

Fold dry ingredients into wet ingredients in two parts, folding carefully with a spatula until just combined. Avoid overmixing to keep the bread tender.

Fold in the toasted walnuts, reserving a handful to sprinkle on top.

Pour batter into the prepared loaf pan and smooth the top. Sprinkle the reserved walnuts evenly on top.

Bake for 55-65 minutes, or until a toothpick inserted in the center comes out clean or with a few moist crumbs. Tent with foil halfway through baking if the top browns too quickly.

Cool in the pan for 10-15 minutes. Use the parchment overhang to lift the bread out and transfer to a cooling rack to cool completely before slicing.