Preheat the oven to 350°F (175°C). Grease a 9x5-inch loaf pan or line it with parchment paper.
In a large mixing bowl, mash the bananas until smooth.
Add the melted butter to the bananas, followed by sugar, eggs, and vanilla extract. Stir to combine.
In a separate bowl, whisk together the flour, baking powder, and salt.
Gradually fold the dry ingredients into the banana mixture, mixing until just combined.
Pour the batter into the prepared loaf pan and spread evenly.
Bake in the preheated oven for 55-65 minutes, or until a toothpick inserted into the center comes out clean.
Let the bread cool in the pan for 10-15 minutes, then transfer it to a wire rack to cool completely.