Preheat the oven to 180C/350F. Grease the 9X13 inch rectangular pan and dust with flour to prevent the cake from sticking or line with parchment paper cut to size.
Beat the both sugars, eggs and oil in the bowl of an electric mixer until well combined for about 1 minute. Then add in the flour, cinnamon, baking soda and baking powder, vanilla and salt, mix well but to do not over mix. Then stir in the carrots with a spatula.
Pour the batter into the prepared pan and bake in the preheated oven for 30-35 minutes. Check for doneness with a toothpick, it should come out clean. Cool the cake in the pan for 30 minutes, then turn out on a wire rack and cool completely.
Crush the pistachios into a crumb and set aside till needed.
To make the frosting whip the cold heavy whipping cream with the icing sugar until soft peaks form, then add the pistachio cream (paste) and whip briefly just to combine. Do not over whip.
Spread the pistachio frosting on the sheet cake while making swirls with the back of a spoon or a offset spatula. Cut into 18 squares and decorate each square with a white chocolate carrot or crushed pistachios.