Preheat your oven to 350°F (175°C) and prepare an 8 or 9-inch baking pan by greasing it or lining with parchment paper.

In a large mixing bowl, combine melted unsalted butter, brown sugar, eggs, and vanilla extract, whisking until smooth.

Mash ripe bananas in a separate bowl until smooth, then fold the banana mash into the wet ingredients.

In another bowl, whisk together the all-purpose flour, baking soda, and salt. Gradually fold this into the wet mixture until just combined.

If using nuts, fold them gently into the batter.

Spread the batter evenly in the baking pan and sprinkle granulated sugar on top.

Bake for 45-50 minutes, checking for doneness with a toothpick at 45 minutes.

Let the cake cool for 10-15 minutes in the pan, then slice and serve.