Place rice in a medium-sized bowl and fill with water. Use your hand to swirl the rice around gently until the water becomes murky. Tip the bowl to take out the excess water and repeat until the water runs clear. Strain it and place it in a rice cooker with 1 3/4 cups of filtered water. Choose Normal Regular Rice setting.
Meanwhile, start the jaggery melting process. Heat a saucepan over medium heat and add butter, ghee, cardamom pods, and bay leaf. When the butter and ghee melt (be careful not to let it brown), add 1/3 cup of water and add the jaggery. Let it simmer while stirring to melt all the chunks. When the jaggery has melted and most of the water moisture has evaporated, remove it from heat and set aside.
When the rice is about 3/4th done and heavy steam starts escaping from the rice cooker, open the lid and add the jaggery syrup to the rice cooker. Stir carefully and close the rice cooker again, letting it finish cooking the rice.
After the rice has finished cooking, let the rice rest for 10 minutes before serving. If you feel that the jaggery still hasn't completely melted into the rice, close the lid and let it rest up to an hour. Serve with any garnishing of choice. I like to eat it plain with some crème (malai) on the side.