Preheat the oven to 350°F (175°C).
Grease a 9x5 inch loaf pan and line it with parchment paper.
Whisk the flour, baking soda, and salt together in a medium bowl.
Cream the brown sugar and butter together in a large mixing bowl until light and fluffy.
Beat in the eggs, one at a time, then stir in the mashed bananas and vanilla extract.
Gradually add the dry ingredients to the banana mixture, mixing just until combined.
Fold in the sour cream.
In a small bowl, mix the granulated sugar and ground cinnamon.
Spread half of the batter into the prepared loaf pan.
Sprinkle half of the cinnamon sugar mixture over the batter.
Add the remaining batter on top and sprinkle with the rest of the cinnamon sugar mixture.
Drag a butter knife through the batter to gently swirl the cinnamon sugar throughout.
Bake for 60 minutes, or until a toothpick inserted into the center comes out clean.
Allow the bread to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.