Heat the oven to 350 degrees. Lightly oil a bundt pan & then dust with flour. In a large bowl, whisk together the flour, pumpkin pie spice, baking powder, salt, & baking soda.
In a medium bowl, whisk together the eggs, oil, sugars, pumpkin, milk, and vanilla. Add the oil-egg mixture to the flour mixture, mixing until fully incorporated. Stir in the carrots.
Transfer the batter to the prepared bundt pan and bake for 55-60 minutes. Let the cake cool in the pan for 15 minutes before transferring to a wire rack to cool completely. Rinse out the pan & repeat to make the second cake.
After the second cake has cooled, using an electric mixer, beat the cream cheese, butter, & vanilla in a large bowl until smooth. Add the confectioners sugar & beat until fluffy, about 3 minutes.