Wash and peel the carrots. Grate the carrots and measure 3 cups.
On a stove-top, keeping the heat to medium, add ghee in a heavy bottomed kadhai (or non-stick pan).
Once the ghee is melting, add grated carrots and saute.
Keep stirring on low-medium heat till the water evaporates from the carrots. This might take around 10-15 minutes.
Add milk and ground cardamom to the grated carrots, keeping the heat to medium, bring the mixture to a boil.
Reduce the heat to low-medium, and keep on stirring the mixture after every few minutes, till the milk reduces to more than half. This will take another 15 minutes or so.
Once almost most of the milk is evaporated, and you are left with the thick mixture, add the jaggery powder. After adding jaggery powder, reduce the heat. This is the point when you have to keep on stirring the mixture thoroughly, cleaning the sides of the pan/kadhai, else there will be chances of the halwa sticking to the pan.
Test the final sweetness, add some more jaggery powder if you think is required.
Top the halwa with chopped nuts of choice. I have used chopped cashews, sliced blanched almonds and raisins.
Give it a final mix. Turn off the heat and enjoy hot and healthy gajar ka halwa!