Rinse and dry the carrots. Peel and trim the top and bottom ends. Grate the carrots using a hand grater or a food processor.
Add half of the ghee to a heavy bottom pan. Add grated carrots and cook over medium heat for 5 minutes as the color of the carrots change to a brighter oranger. This step helps remove some of the excess moisture from the carrots.
Stir in milk and cook on medium heat, stirring frequently. Scrape the milk solids as they start forming on the sides of the pan and mix them in the carrots. Cook until the milk is 90% evaporated, stirring frequently making sure the milk is not getting stuck to the bottom of the pan. This process can take 50 minutes to an hour.
Add sugar, remaining ghee, cardamom powder, and half of the chopped nuts. Mix everything well. The halwa will become a bit watery as the sugar melts in. Keep cooking until the halwa thickens a bit and most of the remaining milk evaporates - it takes about 5 to 10 minutes. Turn the heat off. Garnish with remaining nuts and enjoy warm or cold.