Preheat the oven to 350°F (175°C). Grease a 9×5 inch loaf pan with butter or non-stick spray.
In a large mixing bowl, mash the ripe bananas with a fork until smooth.
Add the granulated sugar, melted butter, eggs, and vanilla extract to the mashed bananas. Mix well until combined.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the banana mixture, stirring gently until just combined.
Fold in the sour cream until the batter is smooth and well incorporated.
Pour the batter into the prepared loaf pan and spread it evenly.
Bake in the preheated oven for 60 minutes, or until a toothpick inserted into the center comes out clean.
Remove the banana bread from the oven and let it cool in the pan for 10 minutes.
Transfer the bread to a wire rack to cool completely before slicing and serving.