Preheat your oven to 350°F (175°C). Grease a small loaf pan or line it with parchment paper.
In a mixing bowl, mash the ripe banana with a fork until smooth. Add the granulated sugar, brown sugar, and melted butter. Mix until well combined.
Stir in the egg and vanilla extract until fully incorporated.
In a separate bowl, whisk together the baking soda, salt, and flour. Gradually add the dry ingredients to the wet mixture, stirring just until combined. Be careful not to overmix.
If desired, fold in the chopped walnuts or chocolate chips.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Bake for 50-60 minutes, or until a toothpick inserted into the center comes out clean. Let the banana bread cool in the pan for about 10 minutes before transferring it to a wire rack to cool completely.