Preheat the oven to 350°F (175°C). Grease a 9x5-inch loaf pan, or line it with parchment so the loaf lifts out easily.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, and salt. Set aside.
In a large bowl, whisk the brown sugar into the melted butter and oil until smooth. Whisk in the eggs one at a time, then the vanilla.
Stir in the mashed bananas until combined.
Add the dry ingredients to the wet and fold with a spatula until just combined. A few small flour streaks are fine. Overmixing makes the bread tough.
Fold in the nuts, if using.
Scrape the batter into the prepared pan and smooth the top. Bake for about 60 minutes, until the top is deep golden brown and a toothpick inserted in the center comes out clean or with a few moist crumbs. If the top is browning too quickly, tent loosely with foil for the last 15 minutes.
Let the bread cool in the pan for 15 minutes, then turn it out onto a wire rack. Cool at least 30 minutes more before slicing so it sets up and cuts cleanly.