Soak the yellow and black mustard in warm water for 15 minutes. Drain the mustard. Make a smooth paste of the mustard with 3 green chillies, a pinch of turmeric powder and a couple of grains of rice. (If you choose, you can as well add one or two garlic cloves while making the mustard paste.)
Cut each eggplant lengthwise into 4 pieces. Smear with a little salt and turmeric powder. Keep aside for 15-20 minutes. Heat oil in a pan and fry the eggplant till golden brown. Remove from the oil with a slotted spoon and place on a kitchen towel to soak any excess oil.
In the same oil, add kalonji and slit green chilies, allow them to splutter. Add the ginger paste and saute for a minute. Now lower the flame and add the mustard paste, whipped yogurt, the remaining turmeric powder, salt and sugar, give it a hearty stir and let it cook for 3-5 minutes.
Gently add in the fried eggplant and half a cup of warm water. Cover and cook for a further 5-7 minutes. The gravy should be of a medium consistency, neither too thick nor too thin.
Serve hot with rice.