Peel the raw papaya and immerse in a bowl of water for 10 minutes. This is to make it easier to cut without all the sap sticking to the fingers. Remove and cut into a 1 cm dice. Boil the diced raw papaya in 2 cups of water with salt and turmeric for 15 minutes, until cooked, but not mushy. Alternatively, place in a pressure cooker with 1 cup water with salt and turmeric and pressure cook for 1 whistle.
Pressure cook tur dal with 1.5 cups water and pinch of turmeric. Mash well and keep aside.
For spice paste, heat 1 tsp oil in a pan. Fry pepper, cumin, red chillies until cumin splutters. Add coconut and lightly toast for 1 minute on low flame along with tamarind piece. Remove all this into a mixer jar when cool. Add 1/4 cup water and grind to a fine paste.
In a cooking pan, combine the mashed cooked dal, cooked raw papaya pieces and the freshly ground spice paste. Season with 1/4 tsp salt or more and bring to a simmer. Thin with a little water to get a pouring consistency of kootu. Transfer to a serving bowl.
Prepare the tempering by heating coconut oil in a small pan or a tadka ladle. Add the red chillies, mustard seeds, urad dal and curry leaves. Once the mustard seeds splutter, transfer this over the prepared kootu.
Serve hot with rice and ghee.