Heat the oven to 350°F. Line a 9x5-inch loaf pan with parchment paper.
Mash the bananas in a large bowl until mostly smooth.
Whisk in the melted butter, brown sugar, egg, and vanilla.
Whisk in the baking soda, salt, and cinnamon.
Fold in the flour just until no dry streaks remain.
Pour the batter into the pan, smooth the top, and sprinkle with the optional brown sugar.
Bake for 55–65 minutes, until a toothpick in the center comes out clean or with a few moist crumbs. Tent with foil if the top browns too fast.
Cool in the pan for 10 minutes, then move to a wire rack and cool at least 30 minutes before slicing.