Preheat oven to 350°F (175°C). Grease and flour a 9x5 inch loaf pan.
In a large bowl, whisk together melted butter and sugar. Beat in eggs one at a time, then stir in mashed bananas, sour cream, and vanilla extract.
In a separate bowl, whisk together flour, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Gently fold in the blueberries.
Pour the batter into the prepared loaf pan and spread evenly.
Bake for 55-65 minutes, or until a wooden skewer inserted into the center comes out clean. If the top browns too quickly, tent it loosely with foil.
Let the bread cool in the pan for 10 minutes before inverting it onto a wire rack to cool completely.
Notes
This banana bread is best served at room temperature. It can be stored in an airtight container for up to 3 days.