Preheat the oven to 350°F (175°C). Grease a 9×5 inch loaf pan with butter or non-stick spray.
In a medium bowl, whisk together the all-purpose flour, baking soda, and salt. Set aside.
In a large bowl, cream the softened butter and granulated sugar together with an electric mixer until light and fluffy, about 3 minutes.
Beat in the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
Add the mashed bananas and sour cream to the wet ingredients and mix until combined.
Gradually add the dry ingredients to the wet ingredients, folding gently with a spatula until just combined. Do not overmix.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
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 allow it to cool in the pan for 10 minutes.
Transfer the bread to a wire rack to cool completely before slicing and serving.