Preheat oven to 350 degrees F. Butter and flour a 1-pound loaf pan. (Mine is 8 1/2" x 4 1/2" x 2 3/4" high.)
In a skillet, melt butter over medium heat, swirling the pan occasionally, until melted. Continue cooking, swirling frequently, until the milk solids are golden brown and the butter has a nutty aroma. (Watch carefully! Brown butter can burn easily.)
Pour the brown butter into a bowl, leaving behind any particularly dark sediment in the pan. Set aside to cool slightly while you mix the rest of the ingredients for the batter.
In a medium bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Set aside.
In a second bowl, whisk together eggs, brown sugar, and granulated sugar until light. Whisk in vanilla, sour cream, cooled brown butter, mashed bananas, and orange zest (if using).
Add the dry ingredients to the wet ingredients, mixing just to combine (a few streaks of flour are ok; over-mixing won't yield as tender a crumb). Fold in chopped nuts, if using.
Bake 50-60 minutes, until a cake tester inserted in the center comes out with just a few crumbs attached. Cool the banana bread for 10 minutes in the pan before transferring to a wire rack to cool completely.
Store, tightly-wrapped or covered at room temperature for up to 2 days, in the refrigerator for up to a week, or the freezer for up to 2 months.