Preheat the oven to 350°F (175°C) and grease a 9x5-inch loaf pan.

In a large bowl, stir together sugar and melted butter until well combined. Add eggs and vanilla, mixing thoroughly.

In a separate bowl, combine flour, baking soda, and salt. Gradually mix the dry ingredients into the butter mixture until smooth.

Fold in sliced bananas, sour cream, and chopped walnuts, then pour the batter into the prepared pan.

Bake in the oven for approximately 1 hour or until a toothpick inserted in the center comes out clean.

Cool the loaf in the pan for 10 minutes, then invert onto a wire rack to cool completely.