Preheat the oven to 350°F and line an 8x8-inch square metal baking pan with parchment paper, securing the sides with binder clips.

Combine flour, granulated sugar, ground pistachios, baking powder, baking soda, salt, and spices in a medium bowl and whisk to blend evenly.

In another medium bowl, combine grated carrots, brown sugar, oil, thinned out yogurt or sour cream, egg, and vanilla, then whisk until combined.

Make a well in the center of the dry ingredients and add the wet mixture. Gently fold until evenly combined; the batter will be glossy but thick.

Spread the batter evenly into the prepared pan and bake for 20-25 minutes until a skewer inserted into the center comes out clean. Let cool for 20 minutes in the pan, then transfer the cake to a cooling rack.

In a large bowl, beat soft cream cheese until very smooth. Add 2 tablespoons of cream and beat until smooth.

Gradually add remaining cream a few tablespoons at a time, beating well after each addition until soft peaks form.

Gradually beat in sugar until thickened to a spreadable consistency, then mix in lemon juice and vanilla extract.

Spread the frosting over the cooled cake and top with more crushed and chopped pistachios before serving.

For carrot decorations, mix ¼ cup of cream cheese with 1 teaspoon of sugar, then mix in heavy cream until it reaches piping consistency. Divide and color one portion orange and the other green, then pipe little carrots onto the cake.