Preheat the oven to 180°C (356°F), grease a baking tin.
Beat eggs and sugars, then add oil.
Mix in flour, baking powder, spices, pecans, and carrots.
Pour into the tin and bake for 30-40 minutes. Cool for 15 minutes before removing from the tin.
Mix cream cheese, heavy cream, and powdered sugar until smooth.
Spread over the cooled cake.
