Heat the oil in a wok or skillet. Add the mustard seeds and asafoetida. When the mustard sputters, add the udad dal, stir fry for a minute until lightly golden-brown, then add turmeric powder, green chillies, and curry leaves.
Add the shredded cabbage and stir it all together very well. Add some salt. This will help the cabbage soften without having to add extra water.
Stir-fry for about 10 minutes or until the cabbage is tender but still has a bite to it. If you like your cabbage really tender, let it go for a few more minutes. Be sure to stir often so it doesn't stick to the bottom of the pan and burn.
Garnish, if desired, with some shredded coconut and coriander leaves.
Nutrition estimate per serving (for 6 servings): Calories 22, Total fat 0.9 grams, Potassium 146 mg, Cholesterol 0 mg, Sugar 0 g, Dietary Fiber 1.4 grams, Protein 0.9 grams