Combine the rinsed toor dal, 3 cups of water, and turmeric powder in a saucepan. Bring to a boil, then reduce heat and simmer uncovered for about 25 to 30 minutes until the lentils are completely soft and easily mashed with a spoon.

In a separate large pot, combine the mixed vegetables, tamarind water, and salt. Bring to a boil over medium-high heat, then cover and simmer for 15 minutes until the vegetables are tender.

Mash the cooked toor dal until smooth. Stir the mashed dal into the pot with the cooked vegetables. Add the sambar powder and red chili powder, stirring well to combine.

Bring the combined sambar mixture to a gentle boil over medium heat, then reduce heat and let it simmer uncovered for 10 minutes to meld the flavors.

Heat the cooking oil in a small pan over medium heat. Add the mustard seeds and let them sputter. Add the broken dried red chilies, fresh curry leaves, and hing, stirring for 10 seconds until fragrant.

Pour the hot tempering mixture directly into the simmering sambar, cover the pot immediately to trap the aromas for 1 minute, then stir well before serving.