Preheat the oven at 175ºC/350ºF conventional oven and grease a 21,5 x 11,5 cm /8,5x4,5 inch loaf pan lined with parchment paper.
Grate the carrots and weigh it out. Set it aside.
In a large bowl, stir together the brown sugar, granulated sugar and oil.
Add the eggs and mix it in until combined.
In a separate bowl, sift together all-purpose flour, baking powder, baking soda, cinnamon, all spice, nutmeg, cloves and salt. Add half the dry ingredients to the wet ingredients and mix it together until combined.
Then add the sour cream and vanilla extract and mix until combined. Add the other half of the dry ingredients to the wet ingredients and mix until combined.
Finally add the grated carrots, using a rubber spatula, gently fold it together with the batter until evenly combined.
Pour the cake batter into the prepared loaf pan. Take a butter knife and insert it into the top of the batter in the loaf pan and run it a straight line down the middle of the batter.
Bake it for 1 hour 5-15 minutes. Let the cake cool on a cooling rack. After 10 minutes, gently remove the cake from the cake tin and let it cool down completely.
Note: If the baking is larger or smaller loaf pan, it can affect the baking time, therefore bake it until a cake tester or tooth pick comes out clean.
Once the loaf is completely cooled down, take the butter and cream cheese out of the fridge 10 minutes before starting. Cut the butter into cubes. Sift the powdered sugar.
In your stand mixer, using the paddle attachment or using a hand mixer, start by creaming the butter for 5 minutes on high speed. Scrape down the sides of the bowl and give it another mix for 2 minutes.
Add the vanilla bean paste and cream cheese and cream it together with the butter for 1 minute.
Scrape down the sides of the bowl and on low speed, mix the sifted powdered sugar in 2 parts, letting the powdered sugar mix in with butter and cream cheese before adding the next part. Scrape down the sides of the bowl and give it a final mix for 2 minutes.
Add the cream cheese frosting on top of the loaf cake and event it out. Optionally decorate it with carrot sprinkles.
