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Preheat the oven to 350°F (175°C/gas 4).
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Prepare four 8-inch (20-cm) round pans by
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putting 1 tablespoon of coconut oil in each
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one. Using a paper towel, spread the oil
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evenly over the entire inside surface of the
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pan. Then sprinkle the pans with flour and
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empty out the excess.
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In a stand mixer fitted with the paddle
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attachment, combine both sugars, the flour,
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baking soda, salt, cinnamon, and nutmeg.
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Turn the mixer on low (this will “sift” the
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ingredients).
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In separate bowls, add the vinegar to the milk
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and the vanilla to the oil.
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With the mixer running on low, add the milk
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mixture, the oil mixture, and half of the water
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and mix until fully incorporated. Add the
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remaining water and mix until completely
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Blended.
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Add the carrots and mix until evenly
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Distributed.
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Divide batter evenly into the prepared pans
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and bake for 30 to 35 minutes, or until a
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toothpick inserted into the middle of a cake
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comes out clean.
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In a stand mixer fitted with the paddle
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attachment cream the cream cheese and
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butter substitutes until smooth.
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Add the powdered sugar and vanilla on low
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speed and mix until fully incorporated.
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Switch the paddle attachment for the whisk
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attachment and mix on high until light and
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fluffy, 2 to 3 minutes