Add moong dal to a cooker or pot. Dry roast on a medium heat till you get a nice aroma.
Then rinse the dal very well and pour 1½ cup water. If cooking in a pot you may need to add more water.
Pressure cook on a medium flame until soft for 2 whistles.
Optional - Skip this step if the jaggery is clean. While the dal cooks, grate and add jaggery to a small pot with 3 to 4 tbsps of water. Boil it on a medium heat until slightly thick yet runny & of pouring consistency. When done set this aside to cool down.
When the pressure releases, mash the cooked dal slightly. If you prefer smooth payasam then mash it well.
Dal must be fully cooked and should not be even slightly hard. If it is aldente then cook for some more time until soft adding more water if needed.
Pour the thin coconut milk or milk to the dal and bring it to a gentle boil on a low flame.
Add cardamom powder & ginger powder (optional).
Place a filter over the pot and pour jaggery syrup through it to the payasam. Mix it well.
Bring the paruppu payasam to a gentle boil. Optionally pour ¼ cup thick coconut milk.
Turn off the stove. Do not boil any longer.
If using regular milk - Cool the jaggery syrup completely before you add here. If you pour the hot jaggery syrup to boiling payasam, it will curdle most of the times. So make sure you cool it. Also turn off the stove and cook no longer.
Heat ghee in a small pan. Fry coconut on a medium high flame until slightly golden. Remove to a small bowl and add cashews to the ghee. Fry until light golden. Then add the raisins and stir until they become plump.
Pour this to the paruppu payasam.