Preheat the oven to 350°F and line an 8x8-inch square metal baking pan with parchment paper, leaving a 2-inch overhang at each side and securing the sides down on the edge of the pan with ¾-inch binder clips.

In a medium bowl, combine flour, granulated sugar, ground pistachios, baking powder, baking soda, salt, and spices. Whisk to blend evenly.

In another medium bowl, combine grated carrots, brown sugar, oil, thinned out yogurt or sour cream, egg, and vanilla. 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 and then transfer the cake to a cooling rack.

To make the frosting, beat soft cream cheese in a large bowl using an electric hand mixer until very smooth. Add 2 tablespoons of cream and beat until very smooth and there are no lumps.

Gradually add the remaining cream a few tablespoons at a time and beat well between additions until it forms soft peaks. Gradually beat in sugar 1 tablespoon at a time 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. The frosting will be soft at first but will thicken further as it sets and after being refrigerated.

For carrot decorations, mix ¼ cup of cream cheese with 1 teaspoon of sugar. Mix in heavy cream a few drops at a time until it reaches a good piping consistency. Divide the mixture into two portions, color one portion orange and the other green. Fill resealable zip-top bags with each icing and pipe little carrots onto the cake.