Preheat oven to 350℉ and grease a 9x9-inch cake pan. Set aside.
Mix the avocado oil, granulated sugar, and brown sugar in a large bowl. Add the vanilla extract and eggs into the bowl. Mix until well combined. Set aside.
Place flour, baking soda, baking powder, salt, cinnamon, and nutmeg, into a bowl and mix to combine.
Add the dry ingredients to the wet ingredients. Once combined, add the shredded carrots and mix to combine.
Transfer the batter to the cake pan—bake for 30-40 minutes or until a toothpick comes out clean. Allow the cake to cool completely before frosting -- about 2-3 hours.
Top the bars with cream cheese frosting and slice them into 12 pieces.