1. Preheat the oven to 175 degrees Celsius (347 degrees Fahrenheit) (fan-assisted).
2. Cut butter into cubes.
3. Whisk butter, sugar, and brown sugar together with a hand mixer until it is white and fluffy.
4. Crack the eggs into a deep plate. Make sure there are no shells!
5. Stir eggs and carrots into the butter/sugar mixture.
6. Mix flour, baking powder, cinnamon, clove, and salt in a bowl.
7. Sift the flour mixture into the mixture and stir it together until it forms a dough.
8. Put the dough in a dish or a springform pan lined with baking paper at the bottom.
9. Bake the cake for 45-60 minutes.
10. Let the cake cool completely, cover the top with cream cheese frosting.
1. Whisk the butter and add powdered sugar a little at a time until it is all incorporated (use a hand mixer or kitchen machine with the paddle attachment).
2. Add vanilla sugar.
3. Whisk until it is fluffy.
4. Add Philadelphia and mix well – optionally, soften the Philadelphia cheese so it doesn't clump!
5. Add lemon juice and grated zest and stir. I also added green food coloring to my frosting.
