Preheat the oven to 350°F (175°C). Grease a 9×5 inch loaf pan or line it with parchment paper.
In a large bowl, combine the mashed bananas, granulated sugar, and melted butter. Mix well.
Add the egg and vanilla extract to the banana mixture and stir until fully incorporated.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, stirring gently until just combined. Do not overmix.
Pour the batter into the prepared loaf pan and spread it evenly.
Bake in the preheated oven for 55 to 60 minutes, or until a toothpick inserted into the center comes out clean.
Remove from the oven and let the banana bread cool in the pan for 10 minutes.
Transfer the bread to a wire rack to cool completely before slicing and serving.