Preheat oven to 350 degrees F (175 degrees C). Grease a 9×13-inch baking pan.
Beat white sugar and vegetable oil together in a bowl using an electric mixer until smooth and creamy; beat in eggs, 1 at a time, mixing well after each addition. Add 1/2 teaspoon vanilla extract and mix.
Combine baking flour, baking powder, baking soda, cinnamon, and salt in a separate bowl; mix into sugar-vegetable oil until batter is smooth. Fold carrots into the batter; pour into the prepared baking pan.
Bake in the preheated oven until a toothpick inserted in the center comes out clean, about 35 minutes. Allow cake to cool completely, at least 30 minutes.
Beat cream cheese and butter together in a bowl using an electric mixer; beat in confectioners’ sugar, a little at a time, until icing is smooth and creamy. Add 1 teaspoon vanilla extract and beat well. Spread icing onto cake.
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