Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a fluted tube pan (such as Bundt®).
Combine cream cheese, sugar, and egg in a bowl for filling, mixing until well blended. Set aside.
Combine flour, sugar, baking soda, cinnamon, and salt for cake in a bowl. Add oil and eggs; mix until moistened. Fold in carrots. Reserve 2 cups of batter; pour remaining batter into the prepared pan. Pour cream cheese mixture over batter. Spoon reserved batter carefully over cream cheese mixture, spreading to cover.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 55 minutes. Cool for 10 minutes; remove from the pan. Sprinkle with powdered sugar.
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