Start by washing and peeling the carrots before grating them finely. Using a medium or fine grater helps the carrots blend into the batter easily. This ensures the cake stays moist and the carrot pieces aren’t too noticeable in texture.
In a bowl, combine the grated carrots, brown sugar, egg, yogurt, oil, and vanilla extract. Whisk everything together until the mixture becomes smooth and evenly combined. This step helps the carrots soften slightly and blend with the sweetness.
Combine the Dry Ingredients
In a separate bowl, whisk together flour, sugar, ground pistachios, baking powder, baking soda, salt, and spices. Mixing these ingredients first ensures the leavening agents and spices distribute evenly throughout the cake.
Pour the wet mixture into the bowl of dry ingredients. Gently fold everything together using a spatula until just combined. Avoid overmixing the batter so the cake stays soft and fluffy.
Transfer the batter into a lined baking pan and spread it evenly. Bake in a preheated oven at 350°F (175°C) for about 20–25 minutes. The cake is ready when a toothpick inserted in the center comes out clean.
Beat the softened cream cheese until smooth using a mixer. Gradually add heavy cream and continue whipping until soft peaks form. Then mix in sugar, lemon juice, and vanilla to create a light, fluffy frosting.
Once the cake has completely cooled, spread the whipped cream cheese frosting evenly on top. Sprinkle chopped pistachios over the frosting for extra crunch and a beautiful finish.