Preheat the oven to 350°F (175°C).Grease and lightly flour a 9x5-inch loaf pan or line it with parchment paper.
In a medium bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, and nutmeg. Set aside.
In a large bowl, mash the bananas.Add the grated carrots, sugars, oil, eggs, and vanilla extract. Mix until smooth and well combined.
Gradually add the dry ingredients to the wet mixture, stirring until just combined. Do not overmix.
Fold in nuts, raisins, or chocolate chips if desired.
Pour the batter into the prepared loaf pan. Smooth the top with a spatula.Bake for 55–65 minutes or until a toothpick inserted into the center comes out clean. Allow the bread to cool in the pan for 10 minutes. Then transfer to a cooling rack to cool completely before slicing.