Preheat the oven to 350°F (175°C). Grease a 9×5 inch loaf pan with butter or non-stick spray.
In a large mixing bowl, combine the mashed bananas, granulated sugar, brown sugar, and melted butter. Mix well until smooth.
Add the eggs one at a time, beating well after each addition.
Stir in the vanilla extract and dark rum until fully incorporated.
In a separate bowl, whisk together the all-purpose flour, baking soda, salt, ground cinnamon, ground nutmeg, and ground allspice.
Gradually add the dry ingredients to the wet ingredients, stirring gently until just combined. Do not overmix.
Fold in the chopped walnuts if using.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Bake in the preheated oven for 55 to 60 minutes, or until a toothpick inserted into the center comes out clean.
Remove the banana bread from the oven and allow it to cool in the pan for 10 minutes.
Transfer the bread to a wire rack to cool completely before slicing and serving.