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Start by heating the oven to 175 degrees Celsius or 350 degrees Fahrenheit. Grab a springform and grease it with butter and a thin layer of flour afterwards.
Grab a large bowl and beat together the eggs, vegetable oil and two teaspoons of vanilla. Mix in the flour, sugar, baking powder & baking soda, a pinch of salt and cinnamon.
Stir in the grated carrots, mix and pour into the prepared springform.
By now the oven should be preheated, so place the springform with the carrot cake batter into the oven for 40 to 50 minutes. You can check if the carrot cake is done when sticking a toothpick into the centre of the carrot cake.
If the toothpick comes out clean, it's done. Let cool for about 10 minutes, then place onto a wire rack and let cool completely.
Grab a medium-sized bowl, add in the butter, cream cheese, one teaspoon of vanilla extract and the powdered sugar. Beat until the mixture is creamy and smooth. Frost the carrot cake with this delicious frosting when the cake has been cooled off completely.