Preheat oven to 350°F (175°C) and grease a 9x5 inch loaf pan.
In a large bowl, mash the bananas until smooth and stir in the melted butter.
Add the baking soda, salt, brown sugar, beaten egg, and vanilla extract; whisk until combined.
Gently fold in the flour and ground cinnamon until no dry streaks remain, taking care not to overmix.
Pour the batter into the prepared loaf pan and smooth the top.
Bake for 60 minutes or until a toothpick inserted into the center comes out clean.
Cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.