Soak tamarind in ¼ cup water for 10-15 minutes. Set aside.
Place cut eggplants in a shallow bowl. Sprinkle with a generous amount of salt. Set aside for 20 minutes.
After 20 minutes, drain and discard the bitter juice. Rinse well under cold running water.
Heat oil in a frypan over medium-high heat. Add eggplants. Saute, stirring occasionally, until browned. Drain on an absorbent towel.
Heat oil in a deep pan over medium-high heat. Splutter mustard seeds and cumin seeds. Add onions and curry leaves, and cook, stirring, for 3-4 minutes, or until browned. Add garlic and green chilies. Stir and cook for a minute, or until fragrant.
Reduce the heat to low. Add ground turmeric, ground coriander, and red chilly powder. Stir and cook again for another 30 seconds, or until fragrant. Add fried brinjal pieces and salt. Mix well.
Squeeze out the pulp from the soaked tamarind (discard the hard bits) and add it to the curry. Add thin coconut milk. Stir well. Increase the heat. Bring to a boil. Reduce the heat and simmer until the sauce starts to thicken (about 3-4 minutes). Add thick coconut milk or coconut cream. Stir and continue to cook until the curry is warmed through.
Remove from heat. Serve with rice and pappadums.