Preheat the oven to 350°. Line two 7-inch diameter cake pans with baking paper. Soak the raisins in hot water. Meanwhile, coarsely chop the hazelnuts.
Combine the grated carrots with the yogurt and Carandini Apple cider vinegar in a bowl.
In a large bowl, whisk flour, cinnamon, ginger, nutmeg, baking powder, salt, and baking soda. With an electric mixer at high speed, beat the eggs with the granulated sugar, brown sugar, and vanilla extract until light-colored and thick, about 4 minutes. Reduce the speed to medium-low and gradually add the oil. Add the dry ingredients in 3 batches, alternating with the carrot mixture in 2 batches, beginning and ending with the dry ingredients; mix until smooth.
Incorporate the raisins and nuts with a rubber spatula. Pour the mixture into the cake pans.
Bake the cakes until a toothpick inserted in the center comes out clean, about 35-45 minutes. Transfer the pans to a wire rack and let the cakes cool for 10 minutes.
Run a knife around the sides of the cakes and place them upside down onto a wire rack, remove the baking paper. Allow to cool completely.
FROSTING AND ASSEMBLY
With an electric mixer at high speed, beat the cream, then add the cream cheese and blend until smooth.
Add the vanilla extract and reduce the speed to low , then gradually add the powdered sugar. Increase the speed to high and beat the frosting until light and fluffy, about 2 minutes.
Spread half the frosting evenly on one cake, place the second cake on top, and coat with tremaining frosting. Let cool 30 minutes to allow frosting to set.