Heat a thin frying pan over a medium-high heat. Cut the brinjal widthways into 12 thick slices, discarding the ends. Lightly brush both sides of each slice with oil and cook for 3-4 minutes on each side until the flesh is soft when pierced. Alternatively, you can cook the brinjal slices under a hot grill or on flame like for bhartha.
Set the cooked brinjal slices aside to cool: they taste best at room temperature.
Meanwhile, heat a small frying pan over a high heat. Dry-fry the cumin seeds for a few seconds, or until they turn dark brown. Remove them from the pan immediately and set aside. When they are cool, grind them to a powder.
Put the tomatoes in a saucepan and cook over a medium heat for 3-4 minutes, stirring occasionally, until they are reduced to a thick sauce, then set this aside to cool.
When the tomato sauce has cooled, add the ground spice and dahi, mix together and season to taste. If you have time, chill the sauce a little.
To serve, lay three slices of the chargrilled brinjal on each of four plates and add a spoonful of the tomato and dahi sauce along the side of each. Garnish with a few fresh coriander leaves and serve.
Ridged, iron grill pans are especially good for cooking brinjal, which otherwise soaks up oil like a sponge.