Rinse the toovar dal until the water runs clear.
Place it in a bowl, cover with hot water, and let it soak for 3–5 hours.
Drain well.
To cook the dal, combine the soaked dal, 6½ cups / 1. 5 liters of water, turmeric, and 1 tablespoon (15 ml / 0.5 fl oz) of butter or ghee in a large saucepan.
Bring to a boil, then reduce the heat, cover, and simmer for about 1½ hours until the dal is very soft. Alternatively, use a pressure cooker with 5½ cups / 1. 3 liters of water and cook for 20–25 minutes.
While the dal cooks, prepare the flavor base. Soak the tamarind pulp in 1 cup / 240 ml of boiling water for 20 minutes.
Squeeze the pulp with your fingers to release the flavor, then strain it through a sieve to get a smooth tamarind juice.
Discard the seeds and fibers.
In a blender, combine the shredded coconut, sugar or jaggery, cayenne pepper, and ⅔ cup / 160 ml (5.4 fl oz) of water.
Blend at high speed until you have a smooth purée.
Heat 4 tablespoons (60 ml / 2 fl oz) of ghee or oil in a separate large saucepan over medium-high heat.
Add the black mustard seeds.
When they begin to pop, add the green chilies and fenugreek seeds and fry for a few seconds until the fenugreek darkens slightly.
Stir in the asafetida and curry leaves, followed immediately by the green beans, carrots, eggplant, tomatoes, and sambar masala.
Sauté the vegetables for about 10 minutes.
Pour the prepared tamarind juice and coconut purée over the vegetables. Partially cover the pan and cook for 10–15 minutes, or until the vegetables are tender.
Once the dal is cooked, whisk it lightly to break it down.
Pour the cooked dal and salt into the saucepan with the vegetables.
Stir well and simmer for 5 more minutes to allow the flavors to meld.
Garnish with fresh coriander or parsley and serve hot.
Using a pressure cooker to cook the dal can reduce the cooking time by more than half, making this dish much quicker to prepare.