Preheat the oven to 350°F (175°C).

In a bowl, whisk the eggs, brown sugar, and white sugar for 5-6 minutes. Add the oil and mix, then add the flour and continue to mix until you have a smooth batter. Add the grated carrots and mix until you have a uniform mixture.

Pour the cake batter into a round 9.5”/24 cm baking pan and bake for about 45-55 minutes or until a toothpick comes out with moist crumbs.

Remove the cake from the oven and let it cool outside until completely cooled.

In the mixer bowl, place the cream cheese, heavy whipping cream, and powdered sugar. Mix until you have a frosting, then add the vanilla pudding and mix again until it's stable.

Once the cake has cooled, remove it from the baking pan and divide it into 3 equal layers. Spread about 1/3 of the frosting on each layer and assemble the cake in layers. Put the cake in the refrigerator for at least 3 hours to set.