Grease a clean working surface (kitchen counter or a large chopping clean board) with ghee and keep it ready. Keep a small bowl of water (at room temperature) ready to test the jaggery syrup. Lightly grease the blade of a knife with ghee and keep it ready.
Dry roast the sesame seeds on a heavy based skillet (tawa) on a medium heat till they turn golden in colour. Don't over roast them as they will burn within seconds and turn bitter. Remove onto a wide plate and let them cool.
Check if the puffed rice is absolutely crisp, if not, place it in a wide microwave safe bowl and microwave it for 30 seconds and allow to cool completely. Once cooled it will turn crisp.
Melt the jaggery in a wide, heavy based wok/kadhai. It needs to become sticky to a point where it hardens upon cooling. To test this, put a drop of the melted jaggery in the bowl of water. If the drop dissolves in the water the jaggery is not yet ready. If you are able to scoop out the drop and make a hard ball using your finger tips, it is ready.
When the jaggery syrup is ready add the puffed rice, sesame seeds and the powdered cardamom and give everything a quick mix. You need to be very quick here as the mixture will harden within minutes. Transfer the entire mixture onto the prepared (greased) working surface.
Quickly pat the surface of the chikki and shape it into a rough rectangle. Using the greased knife lightly score the surface of the chikki into shapes (square/rectangle/bar).
When the chikki is almost cool cut out the shapes. Let the chikki cool completely before storing in an airtight container. Enjoy!