Preheat the oven to 350°F (175°C). Grease a 9-by-5-inch loaf pan or line it with parchment paper.
Mash the ripe bananas in a large mixing bowl.
Add the melted butter, brown sugar, granulated sugar, eggs, and vanilla extract. Stir until well combined.
In a separate bowl, whisk together the flour, baking soda, and salt.
Gradually add the dry ingredients to the banana mixture.
Gently stir until just combined. Do not overmix.
Fold in chocolate chips or chopped nuts if using.
Pour the batter into the prepared loaf pan and smooth the top.
Bake for 50 to 65 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
Cool in the pan for 10 to 15 minutes, then transfer to a wire rack to cool further before slicing.