Preheat the oven to 350°F. Line an 8x8 baking pan with parchment paper.
In a large mixing bowl, combine the melted butter, 1 cup sugar, beaten eggs, and vanilla. Mix until smooth.
Add the bananas and mix until fully incorporated.
Add the flour, baking soda, and salt to the wet mixture. Stir until just combined.
Pour the batter into the prepared pan and spread it evenly.
Generously sprinkle 2–3 tablespoons of sugar over the top of the batter to create a crisp, sweet crust.
Bake for 45 minutes, or until a toothpick inserted into the center comes out clean.
Allow the banana bread to cool in the pan, then slice, serve, and enjoy!