In a medium-sized bowl, whisk together flour, baking soda and cardamom.
In another medium-sized bowl, mix sugar, 3/4 cup of tightly packed halwa, and eggs until well combined.
Mix the ghee and cardamom syrup into the carrot halwa mixture until well combined.
Mix in the flour mixture until fully incorporated.
Fill cupcake liners 3/4 full.
Bake at 350 F for 25 minutes or until a toothpick inserted in the middle of a cupcake comes out clean.
Take the remaining carrot halwa (don't worry, I know that you will have eaten several spoonfulls of it at least - I took that into account) and mix it up using an electic mixer or your own arm strength to incorporate some air into it.
Spread the halwa on top of the cupcakes.
Just before serving, warm the gulab jamun in the microwave and use them to top the cupcakes.