Badanekayi is eggplant in Kannada as you might have already guessed. Mosaru is yogurt. This dish is very easy to make since it has no masala to roast or grind. Goes very well with either rice or rotis. My mother used to roast the eggplant on the gas stove top, but I do it in the oven making it even easier since you can just stick it in the pan, leave it in the preheated oven and walkaway instead of standing and rotating the eggplant on the gas flame. One of my friend's mother used to do it on the gas for a minute or two to get the char on the eggplant and then cook it in the microwave till soft. Here goes my version and I am sure there are many varieties of making the same.
Purple eggplant (big fat kind) - 1 big
Oil - 2 TBSP for tempering and a little for brushing the eggplant and the pan
Mustard seeds - 1/2 tsp
Hing - a generous pinch
Curry leaves - a few
Red chillies - 4 - 5 as per taste broken
Salt - to taste
Yogurt - 1 1/2 - 2 cups
Cilantro - chopped about a TBSP (optional)
Preheat the oven to 375 F. Take an oven proof plate or pan and grease it with oil. Smear some oil on the eggplant all over and Cut into half. Keep them in the pan or plate cut side down. Bake it in the oven for about 45 minutes to an hour. If you are using smaller eggplant, it might get done faster. Keep an eye on it. When done, the skin will have wrinkles all over and a knife can be inserted with no resistance at all. Let it cool enough for you to handle it. When bearable to touch, remove the skin of the eggplant and transfer the pulp to a bowl. Mash it with a fork or a masher. Heat oil in a small pan, when hot add mustard seeds. When the splutter, add red chillies, hing, curry leaves. Pour this onto the mashed eggplant. Add salt to taste and when the mixture comes to room temperature, add yogurt. Mix in chopped cilantro if using. I have given the proportion for yogurt to be a range. Some people like it thick and some people a thinner so that it is nice to mix with rice. Vary it according to your taste. It can be served at room temperature or cold with rotis or rice.