Preheat your oven to 350°F (175°C). Grease a 9x13-inch cake pan.

Grate carrots with a box grater and set aside.

In a large mixing bowl, beat the eggs with an electric mixer or the bowl of a stand mixer. Add the vegetable oil, white sugar, brown sugar, and vanilla extract. Mix well until the sugars are fully dissolved.

Add the dry ingredients: flour, salt, baking soda, and ground cinnamon to the bowl with the wet ingredients. Mix until just combined. Be careful not to overmix.

Fold in the finely grated carrots until evenly distributed throughout the batter.

Pour the cake batter into the prepared 9x13-inch cake pan, spreading it evenly.

Bake in the preheated oven for 40-45 minutes or until a toothpick inserted into the center of the cake comes out clean. Start checking at 35 minutes; cooking times may vary slightly due to the type of pan and oven.

Allow the cake to cool completely before frosting.

In a large bowl, beat together the softened butter and cream cheese until smooth and creamy.

Add the vanilla extract and salt. Mix until well combined.

Gradually add the powdered sugar, one cup at a time, beating well after each addition. Adjust the amount of powdered sugar to achieve your desired sweetness and consistency.

Once the cake has cooled, spread the cream cheese frosting evenly over the top of the cake.

Garnish the cake with chopped nuts, if desired.

Cut into squares and enjoy your delicious, super moist carrot cake!