In a mixing bowl, beat cream cheese and sugar. Add egg; mix well. Refrigerate while making cake batter.
In a mixing bowl, beat the eggs and sugar. Add carrots and oil; beat until blended. Combine the flour, baking soda, cinnamon, pumpkin pie spice, and salt. Add to carrot mixture; mix well. Stir in chopped pecans. Pour 3 cups batter into a greased and floured 10-inch bundt pan or fluted tube pan. Spoon cream cheese mixture over batter. Top with remaining batter.
Bake at 350º for 55 to 60 minutes or until a toothpick inserted near the center comes out clean.
Cool for 10 minutes before removing from pan to a wire rack.
Make Cream Cheese Frosting
In a small mixing bowl, beat the cream cheese, butter and vanilla until smooth.