In a large mixing bowl, whisk together the mashed bananas, shredded carrots, melted butter, brown sugar, granulated sugar, eggs, and vanilla extract until smooth.
In a separate bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, and nutmeg. Gradually add the dry ingredients to the wet mixture, stirring until just combined.
Fold in the chopped walnuts and raisins, if using. Grease a 9x5-inch loaf pan and pour in the batter. Smooth the top with a spatula. Preheat the oven to 350°F (175°C) and bake for 50-55 minutes or until a toothpick inserted in the center comes out clean.
Let the banana bread cool in the pan for 10 minutes before transferring it to a wire rack to cool completely. Slice and enjoy!