Preheat your oven to 350°F (175°C). Grease a 9x5 inch loaf pan and line it with parchment paper, leaving an overhang on the long sides for easy removal.
In a large bowl, mash the bananas with a fork until mostly smooth with a few small chunks remaining. Stir in the melted butter and brown sugar until well combined.
Add the egg, vanilla extract, and sour cream to the banana mixture. Mix until everything is smooth and evenly incorporated.
Add the flour, baking soda, cinnamon, and salt directly over the wet mixture. Fold gently with a spatula until the flour just disappears - a few small streaks are fine.Do not overmix or the bread will turn out tough instead of tender.
Pour the batter into the prepared loaf pan and spread it out evenly. Give the pan a gentle tap on the counter to release any air bubbles.
Bake for 55 to 60 minutes, until the top is deep golden brown and a toothpick inserted into the center comes out clean or with just a few moist crumbs.
Let the banana bread cool in the pan for 10 minutes, then use the parchment overhang to lift it out onto a wire rack. Allow it to cool for at least 20 minutes before slicing.