Heat oil in a heavy-bottomed pan over medium flame. Add the mustard seeds and fry them for few seconds. Once they start to splutter, add the onions and saute until they turn slightly pinkish in hue. Now add the cinnamon and chopped green chillies. Fry for a minute or two. Add the chopped tomatoes and cook for 10 minutes.
Add the ginger, turmeric powder, red chilli powder, coriander powder and stir-fry for a minute. Cook these spices until the oil starts to separate. Add the tamarind paste and 1 cup of water. Simmer for a minute or two.
Add the coconut milk, salt and curry leaves. Stir well and simmer for a minute. Add the eggs and simmer for 3 to 5 minutes over low flame. Stir gently ensuring the eggs stay intact. Garnish with coriander leaves. Serve with hot rice or as a side dish with dosas.