Preheat your oven to 350°F (175°C). Grease an 8x4-inch loaf pan with butter or line it with parchment paper for easy removal.
In a large mixing bowl, mash the ripe bananas with a fork or potato masher until smooth but still slightly chunky.
Add the melted unsalted butter to the mashed bananas and stir to combine. Then mix in the brown sugar, beaten egg, and vanilla extract until everything is well incorporated.
In a separate bowl, whisk together the all-purpose flour, baking soda, and a pinch of salt.
Gradually add the dry ingredients to the wet banana mixture, folding gently with a spatula or wooden spoon. Avoid overmixing to keep the bread tender. Once just combined, fold in the chopped walnuts.
Pour half of the batter into your prepared loaf pan. Drizzle half of the caramel sauce evenly over the batter. Add the remaining batter on top, then drizzle the remaining caramel sauce. Use a knife or skewer to gently swirl the caramel through the batter.
Bake in the preheated oven for 50-60 minutes, or until a toothpick inserted into the center comes out clean or with just a few moist crumbs. Tent with foil if top browns too quickly.
Let the bread cool in the pan for about 10 minutes, then transfer to a wire rack to cool completely before slicing.