Cook the tuvar dal with water and ¼ teaspoon turmeric until very soft and mushy. Set aside.
Place the chopped bitter melon pieces in a saucepan or bowl with enough water to cover. Stir in ¼ teaspoon of turmeric. Cook on the stovetop or in the microwave until the veggies are tender, about 10 minutes. Drain out the water and set aside.
Heat 1 teaspoon oil in a saucepan. Add the chana dal, coriander seeds, red chili peppers and coconut. Saute on low heat for 5-10 minutes or until the coconut is golden-brown and the coriander and dal are a couple of shades darker. Don't leave this unattended and don't do this over high heat as coconut has a tendency to burn. Turn off the heat and stir in the asafetida.
Let the spices and coconut cool on a plate, then blend into a smooth paste with ¼ cup water. Set aside.
Heat the remaining 1 teaspoon oil in the same saucepan. Add the mustard and cumin seeds. When the mustard sputters, add the curry leaves. Saute for a few seconds.
Add the tamarind with ½ cup water. Bring to a boil and let it simmer a couple of minutes.
Add the drained bitter gourd, cooked dal and blended coconut spice paste to the saucepan. Stir in the jaggery and add more water if needed to thin out the dal to your liking.
Add salt to taste. Bring the pitlai to a boil and let it continue to cook over medium heat another five minutes for all the flavors to merge.
Turn off the heat, garnish with cilantro, and serve hot.