Preheat oven to 350°F (175°C) and grease two 9-inch round cake pans with butter or non-stick spray.
In a medium bowl, whisk together the flour, baking soda, salt, and cinnamon until well combined.
In a separate large bowl, whisk together the vegetable oil, granulated sugar, brown sugar, and 1 tsp vanilla extract.
Add eggs to the wet mixture one at a time, whisking thoroughly after each addition.
Gradually fold the dry ingredients into the wet ingredients using a spatula until no streaks of flour remain.
Fold in the grated carrots and chopped pecans.
Divide the batter equally between the prepared cake pans.
Bake for 35 to 45 minutes, or until a toothpick inserted into the center of the cakes comes out clean.
Cool cakes in the pans for 15 minutes, then transfer to a wire rack to cool completely.
Prepare the frosting by beating the softened cream cheese and butter together until smooth and creamy.
Gradually add the powdered sugar and the remaining 1 tsp vanilla extract, beating until the frosting is light and fluffy.
Once the cake layers are completely cold, frost the top of one layer, place the second layer on top, and frost the top and sides of the entire cake.