Cook the dal: In a pressure cooker, combine the toor dal, water, turmeric powder, and salt. Close the lid and cook for 3 whistles or until the dal is tender. Let the pressure release naturally, then open the lid and mash the dal with a potato masher or the back of a spoon.
Make the masala: Heat the oil in a large saucepan over medium heat. Add the mustard seeds and let them crackle for a few seconds. Add the urad dal, chana dal, curry leaves, and dried red chilies and cook for about 30 seconds, until the urad dal and chana dal turn golden brown.
Add the onion and cook until softened and translucent, about 5 minutes. Add the tomato and ginger-garlic paste and cook until the tomato is soft and mushy, about 5 minutes more.
Stir in the sambar powder, coriander powder, cumin powder, and asafoetida. Cook for 1 minute, until the spices are fragrant.
Add the cooked dal and 2 cups of water. Bring to a boil, then reduce the heat and simmer for 10 minutes, or until the flavors have melded.
Stir in the radishes and cilantro. Cook for 5 minutes more, or until the radishes are tender.
Taste and adjust the seasonings as needed. Serve hot with rice, idlis, or dosas.