Preheat your oven to 350°F. Grease a 9x5-inch loaf pan (or an 8 1/2x4 1/2-inch pan) with butter or nonstick spray.

In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set aside.

In a separate large bowl, whisk the melted butter and granulated sugar together until smooth.

Whisk in the eggs one at a time, then stir in the mashed bananas, sour cream, and vanilla extract until fully combined.

Pour the banana mixture into the flour mixture. Fold gently with a rubber spatula until no streaks of flour remain. If using nuts, fold them in at this point. Do not overmix.

Pour the batter into the prepared loaf pan and spread it evenly. Bake for 50 to 58 minutes, or until a toothpick inserted in the center comes out clean or with a few moist crumbs.

Let the bread cool in the pan for 10 to 15 minutes. Run a knife around the edges, then invert onto a wire rack to cool completely.

Allow the bread to cool on the rack for about 30 minutes, then transfer to an airtight container. Store at room temperature for up to 3 days, or refrigerate for longer freshness.