Preheat your oven to 350°F (175°C) and prepare two 8-inch round baking pans by greasing and flouring them, then lining the bottoms with parchment paper.

In a large mixing bowl, mix together all-purpose flour, granulated sugar, packed light brown sugar, ground cinnamon, baking powder, baking soda, and salt until well combined. Mix until well combined.

Add the canola oil and melted unsalted butter to the dry ingredients, stirring until a thick batter forms.

Add the eggs one at a time, beating well after each addition to ensure full incorporation before adding the next. Then, mix in the vanilla extract.

Gently fold in the grated carrots and chopped nuts (if using), ensuring they are evenly distributed throughout the batter.

Divide the batter evenly between the prepared cake pans, spreading it out into smooth, even layers.

Bake in the preheated oven for 40-45 minutes or until a toothpick inserted into the center of the cakes comes out clean.

Let the cakes to cool in the pans for 15 minutes before transferring them to wire racks to cool completely.

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

Add the vanilla extract and salt to the cream cheese mixture, continuing to beat until well combined.

Gradually add the powdered sugar, mixing on low speed until the frosting is smooth and creamy.

Once the cakes have cooled completely, spread a generous layer of frosting on top of one cake layer.

Position the second cake layer on top, then generously frost the top and sides of the cake with the remaining frosting.

Optional: Decorate the cake with additional chopped nuts or shredded carrots, if desired.

Serve and enjoy your delicious homemade Cheesecake Factory Carrot Cake.