Preheat your oven to 350°F (175°C). Grease and line a 9×13-inch baking pan or two loaf pans if you prefer a banana loaf style.
In a medium bowl, whisk together flour, baking soda, baking powder, cinnamon, nutmeg, and salt.
In a large mixing bowl, beat together the granulated sugar, brown sugar, and oil until combined. Add eggs one at a time, mixing well after each addition. Stir in mashed bananas and vanilla extract until smooth.
Gradually fold the dry ingredients into the wet mixture until just combined. Gently stir in grated carrots and nuts if using. Do not overmix.
Pour the batter into the prepared pan and smooth the top evenly.
Bake for 35–45 minutes (less for loaf pans, more for larger pan), or until a toothpick inserted in the center comes out clean.
Allow the cake to cool completely before frosting.
To make the frosting, beat cream cheese and butter until creamy. Gradually add powdered sugar and vanilla, mixing until fluffy. Spread evenly over the cooled cake.
Slice and serve as a delicious banana dessert that feels both classic and new.