Preheat oven to 350°F (175°C) and grease a 9x5 inch loaf pan with butter or non-stick spray.

In a large mixing bowl, mash the bananas until smooth, then stir in the melted butter.

Add the brown sugar, egg, vanilla extract, and grated carrots to the banana mixture and whisk until well combined.

In a separate medium bowl, sift together the flour, baking soda, salt, cinnamon, ginger, and nutmeg.

Gradually fold the dry ingredients into the wet ingredients using a spatula until just combined; do not overmix.

Fold in the chopped walnuts if desired.

Pour the batter into the prepared loaf pan and smooth the top with a spatula.

Bake for 50 to 60 minutes, or until a toothpick inserted into the center comes out clean.

Allow the bread to cool in the pan for 10 minutes before transferring to a wire rack to cool completely.