Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 9x13 inch pan.

Beat sugar, oil, eggs, and 2 teaspoons vanilla together in a large bowl with an electric mixer until well combined. Mix in flour, baking soda, baking powder, cinnamon, and salt. Stir in carrots. Fold in pecans. Pour into the prepared pan.

Bake in the preheated oven until a toothpick inserted into the center of the cake comes out clean, about 40 minutes. Let cool in the pan for 10 minutes, then turn out onto a wire rack and cool completely.

To make the frosting: Beat butter, cream cheese, confectioners' sugar, and 1 teaspoon vanilla together in a large bowl with an electric mixer until smooth and creamy. Stir in chopped pecans. Frost the cooled cake.