Preheat your oven to 350°F (175°C). Use a bit of butter or non-stick spray to grease a 4×8-inch loaf pan. In a large mixing bowl, peel the ripe bananas and mash them with a fork until they reach a smooth consistency. A few small lumps are perfectly fine and add texture to the final bread.
Stir the melted butter into the mashed bananas. Add the sugar, beaten egg, and vanilla extract. Mix everything until well combined. Sprinkle the baking soda and salt over the mixture and stir. Finally, gently fold in the all-purpose flour. Be careful not to overmix the batter; stir only until the flour streaks disappear to keep the bread tender.
Pour the batter into your prepared loaf pan and smooth the top with a spatula. Place the pan in the center of the oven and bake for 50 to 60 minutes. Check for doneness by inserting a toothpick into the center; it should come out clean or with just a few moist crumbs. Remove the bread from the oven and let it cool in the pan for 10 minutes. Transfer the loaf to a wire rack to cool completely before slicing.