Heat a pan and add oil (or ghee, as preferred). I used sunflower oil, but any vegetable oil would suit.
When the oil is hot, add mustard seeds, let them crackle. Add cumin seeds, keeping the stove on low heat.
Continuing to keep the heat low, add green chillies and let them sputter.
Add curry leaves - Fresh curry leaves usually sputter and crackle when added to hot oil, so step away as you do when chilies are added.
Add the slices of onion and sauté till the onions are translucent, stirring occasionally so they do not catch at the bottom of the pan.
Add the slices of peeled arbi (colocasia). Add the red chilli powder. Sauté for about 3-4 minutes in the spices already in the pan, stirring briskly so that the arbi is coated with the spices. The arbi is already boiled, so it does not need to cook for long, however let the raw smell of the chilli dissipate.
Keeping the stove on low heat, add the curd you have kept ready with flour, turmeric, cumin powder and salt. Whisk it again and if thick, add a tablespoon of water. Bring to a slow boil. Keep it on a simmer for 5 minutes till the raw smell of the flour goes away, and then remove the pan from the stove. Transfer the arbi ki kadhi immediately from the hot pot to a serving vessel and serve with rice or with chapatis.